user16651: I raised a flag on this question yesterday.
How small can the human eye distinguish given the distance?
https://biology.stackexchange.com/questions/40739/how-small-can-the-human-eye-distinguish-given-the-distance
The question has been closed and deleted. Yet my flag was declined. The question was an optics question which clearly should have been addressed on Physics SE.
Whether or not you agreed that the question should be migrated, you obviously agreed that it did not belong on Biology SE. In that case a valid flag should not be rejected.
It becomes really annoying and discourages community moderation. 

user6: Declining flags isn't an entirely objective process, the rules are pretty fuzzy and there are many differences in how moderators handle this. There are also some issues with the tools and the flagging process in general that lead to situations where reasonable flags are sometimes declined. Most users, including many moderators, are also not familiar with all the details of the whole flagging system. They are not documented well and have changed signficantly over time.
Declining flags is also not meant as negative as it is often perceived. The main purpose is to educate user on how to flag more effectively.
The big principle of flagging that was already mentioned is that you shouldn't use flags for issues that you can address yourself and that don't need moderator intervention. If a question should be closed, use a close flag or close vote as those are handled by the review queues.
Now, regarding the specific flags mentioned in your post and WYSIWYG's post:
The flag about migration to Physics is a reasonable flag in my opinion. Migration is something the community can't do, so involving a moderator makes sense. But I can see declining the flag if the moderator considers this question to be either too poor to migrate, or not off-topic at all on our site. I would probably have validated the flag, but not migrated this post if I had handled it. But I can easily see myself declining flags in rather similar circumstances. The question was self-deleted by the author minutes after your comment and flag, so this isn't any evidence that it was off-topic here. 
Regarding flag 1, I would have declined this one as well. You should have downvoted and/or flagged to close the question, there is no need for a moderator flag in this case.
Regarding flag 2, this isn't really VLQ in my opinion. Closing it because of the vagueness of the question is probably justified, but again no reason for a moderator flag. 
Regarding flag 3, there was no reason to act on that question in my opinion. Even if the user was a creationist, the question wasn't really problematic. And the comments were unnecessarily hostile, I removed them in the meantime. 
Regarding flag 4, I can't argue that this isn't VLQ, it clearly is. I generally prefer using close flags on questions instead of VLQ, I don't think the VLQ flag should even be available on questions. But as my own opinion here differs from the guidance on the flagging dialog, I would not decline such flags in cases of truly VLQ posts.

user3340: First, let me clarify that the post that is mentioned in the question was already deleted when I reviewed the flag. From the timeline:
Nov 18 at 5:54  flag        cleared     WYSIWYG♦     Declined: flags should only be used to make moderators aware of content that requires their intervention
Nov 18 at 2:42  history     deleted     user3667089     via Vote
Nov 18 at 2:40  flag        PostOther   AMR          This question is off-topic because it is an optics question and is better addressed on Physics S.E.
Nov 18 at 2:38  comment     added       AMR          You are going to want to look up optics formulas and that would be Physics related. 

Moreover, you raised the flag almost immediately after posting the comment. I feel that scientifically this post also had a biological angle and therefore migration is not necessary. I still could have declined the flag for "not finding evidence in support of it". However, since the post was already deleted I used the abovementioned reason. You should understand that cases like this are not that common.
Since you think that many of your flags have been declined for unjust reasons I'll explain the cases of last four of your flags that have been declined as "flags should only be used to make moderators aware of content that requires their intervention".

Oct-25: Why to use transgenic mice in ALS models?  Flagging reason: "While this technically isn't a homework question, it is clear that the OP has done none of their own research of the topic of Transgenic Mouse Models."  Decline reason: For poor effort you should downvote or if the post is really bad you may vote to close as "homework". Else you can vote to close with a custom reason. Whether or not these kind of questions should be closed, has been extensively debated upon.
Oct-30: https://biology.stackexchange.com/q/40072/3340  Flagging reason: Very low quality Decline reason: VLQ flag should be raised when the content is so poor that it cannot be salvaged by editing (see https://meta.stackexchange.com/a/93606/272208). You did not even leave a comment to ask OP to improve their question. In any case this post does not need moderator intervention. Close/down- vote should have sufficed. 
Nov-4: Please explain this disrepancy about ageing  Flagging reason: "... this is just an attempt by a creationist to poke holes in evolutionary theory by what they presume is an inconsistency without actually knowing the finer details of the molecular processes involved or how they relate to organismal survival. For that reason this post should be closed."  Decline reason: I should have actually declined this for not finding an evidence in support of the flag. However, you claim that OP is basing their question on creationist beliefs. This you also commented to which OP has replied that they are not citing the Bible or any other religious book. This flag was unnecessary. Again, you should have voted to close or downvoted if you think background research is not done. 
Nov-16: https://biology.stackexchange.com/q/40671/3340  Flagging reason: VLQ  Decline reason: Same as in case 2

Some of the flags have not been declined by me (in case if you are assuming that I am the evil despot here.)

Regarding AliceD comment: It may be me, but you have been mod-closing many questions - you shouldn't bring up a (very valid) argument that you are not practicing. Further, AMR's argument goes beyond this specific case.
When I close questions, I close them for their content, after reading the posts. Most closures have been for duplicates or very broad. These are the times actually when I wish I do not have a binding vote. Anyway, I shall try to limit myself to just post comments when I feel a certain post deserves closure for scientific content. Flags, however, are a different matter. Moderator is not supposed to verify the scientific authenticity of the content. If AMR's argument goes beyond this specific case then it is expected that they explicitly point out at least a few instances when their flags have been unjustly declined. 

Addendum
I was unaware that you could not cast a close vote. However, when you think a question should be closed then you can flag the question for closure. These flags are dealt by the community. Moderator attention flags are to be used only in very specific situations. Yes, migration is a valid reason but it is good to wait for the community's verdict on whether the question is really off-topic. I would suggest that such questions be VTCed as off-topic with a custom reason saying that it belongs to another site. But as such there is no harm in calling for mod attention for migration when you are sure enough. The flag may be rejected, though. Better to comment first and ask OP for clarification in doubtful cases.

user1306: I am not a mod here so I don't have access to your flagging history. However, based on the public data from your profile, we can see that:

You have raised a total of 91 helpful flags;
You have cast a measly 14 downvotes.

Based on that and on the discussion we had about this in the chat room, you seem to feel that flags are the first line of defense for the site. They aren't. The first line of defense is voting. That's precisely why downvoting questions carries no rep penalty and why the first reason given for downvoting is lack of research:

In your case, since you don't have the rep to close vote directly, flagging for closure is perfectly OK. However, you should really try to avoid using the custom mod flag unless none of the other reasons apply. 
So, of the 5 flags cited by WYSIWYG, I would also have rejected 1 and 3. In the case of 1, lack of research is no reason to flag, it's a reason to downvote. Raising flags on posts that don't actually need moderator intervention is just creating work for the moderators for no reason. Just downvote and move on. If you must, flag to close as homework but don't flag for mod attention. What was the mod supposed to do? We try to avoid unilaterally closing questions since mod votes are binding. It is far better to let the community decide unless the question is an egregious example, completely off topic or whatever. 
Your 3rd flag was because, in your opinion, the question was from a creationist. That is no reason to flag at all! First off, we have not made creationism or ID explicitly off topic. It is not mentioned anywhere in the help center. There have been some meta discussions (1,2, 3) on the subject but none has had enough votes to reach a consensus and, in any case, it hasn't been made official, so it isn't a valid reason to close, let alone flag. 
I should also point out that the golden rule for migrating questions is don't migrate crap. I don't have the rep to read the deleted question you mention but if it was both off topic here and a bad question, then it shouldn't be migrated and the mods were right to decline your flag. We can't use other sites as our dumping ground just like we wouldn't like to receive crap questions from elsewhere. Therefore, that the question was eventually deleted is no indication that your flag was valid. 
In conclusion, please try and only flag what needs to be flagged. Your first choice for bad questions should always be a downvote and flagging should only be a last resort. 

16651: <p>I raised a flag on this question yesterday.</p>

<p><strong>How small can the human eye distinguish given the distance?</strong></p>

<p><a href="https://biology.stackexchange.com/questions/40739/how-small-can-the-human-eye-distinguish-given-the-distance">https://biology.stackexchange.com/questions/40739/how-small-can-the-human-eye-distinguish-given-the-distance</a></p>

<p>The question has been closed and deleted. Yet my flag was declined. The question was an optics question which clearly should have been addressed on Physics SE.</p>

<p>Whether or not you agreed that the question should be migrated, you obviously agreed that it did not belong on Biology SE. In that case a valid flag should not be rejected.</p>

<p>It becomes really annoying and discourages community moderation. </p>
 6: <p>Declining flags isn't an entirely objective process, the rules are pretty fuzzy and there are many differences in how moderators handle this. There are also some issues with the tools and the flagging process in general that lead to situations where reasonable flags are sometimes declined. Most users, including many moderators, are also not familiar with all the details of the whole flagging system. They are not documented well and have changed signficantly over time.</p>

<p>Declining flags is also not meant as negative as it is often perceived. The main purpose is to educate user on how to flag more effectively.</p>

<p>The big principle of flagging that was already mentioned is that you shouldn't use flags for issues that you can address yourself and that don't need moderator intervention. If a question should be closed, use a close flag or close vote as those are handled by the review queues.</p>

<p>Now, regarding the specific flags mentioned in your post and WYSIWYG's post:</p>

<p>The flag about migration to Physics is a reasonable flag in my opinion. Migration is something the community can't do, so involving a moderator makes sense. But I can see declining the flag if the moderator considers this question to be either too poor to migrate, or not off-topic at all on our site. I would probably have validated the flag, but not migrated this post if I had handled it. But I can easily see myself declining flags in rather similar circumstances. The question was self-deleted by the author minutes after your comment and flag, so this isn't any evidence that it was off-topic here. </p>

<p>Regarding flag 1, I would have declined this one as well. You should have downvoted and/or flagged to close the question, there is no need for a moderator flag in this case.</p>

<p>Regarding flag 2, this isn't really VLQ in my opinion. Closing it because of the vagueness of the question is probably justified, but again no reason for a moderator flag. </p>

<p>Regarding flag 3, there was no reason to act on that question in my opinion. Even if the user was a creationist, the question wasn't really problematic. And the comments were unnecessarily hostile, I removed them in the meantime. </p>

<p>Regarding flag 4, I can't argue that this isn't VLQ, it clearly is. I generally prefer using close flags on questions instead of VLQ, I don't think the VLQ flag should even be available on questions. But as my own opinion here differs from the guidance on the flagging dialog, I would not decline such flags in cases of truly VLQ posts.</p>
 3340: <p>First, let me clarify that the post that is mentioned in the question was already deleted when I reviewed the flag. From the timeline:</p>

<pre><code>Nov 18 at 5:54  flag        cleared     WYSIWYG♦     Declined: flags should only be used to make moderators aware of content that requires their intervention
Nov 18 at 2:42  history     deleted     user3667089     via Vote
Nov 18 at 2:40  flag        PostOther   AMR          This question is off-topic because it is an optics question and is better addressed on Physics S.E.
Nov 18 at 2:38  comment     added       AMR          You are going to want to look up optics formulas and that would be Physics related. 
</code></pre>

<p>Moreover, you raised the flag almost immediately after posting the comment. I feel that scientifically this post also had a biological angle and therefore migration is not necessary. I still could have declined the flag for "not finding evidence in support of it". However, since the post was already deleted I used the abovementioned reason. You should understand that cases like this are not that common.</p>

<p>Since you think that many of your flags have been declined for unjust reasons I'll explain the cases of last four of your flags that have been declined as "flags should only be used to make moderators aware of content that requires their intervention".</p>

<ol>
<li>Oct-25: <a href="https://biology.stackexchange.com/q/39924/3340">Why to use transgenic mice in ALS models?</a> <br> <strong>Flagging reason</strong>: "While this technically isn't a homework question, it is clear that the OP has done none of their own research of the topic of Transgenic Mouse Models." <br> <strong>Decline reason</strong>: For poor effort you should downvote or if the post is really bad you <strong>may</strong> vote to close as "homework". Else you can vote to close with a custom reason. Whether or not these kind of questions should be closed, has been extensively debated upon.</li>
<li>Oct-30: <a href="https://biology.stackexchange.com/q/40072/3340">https://biology.stackexchange.com/q/40072/3340</a> <br> <strong>Flagging reason:</strong> Very low quality <br><strong>Decline reason:</strong> VLQ flag should be raised when the content is so poor that it cannot be salvaged by editing (see <a href="https://meta.stackexchange.com/a/93606/272208">https://meta.stackexchange.com/a/93606/272208</a>). You did not even leave a comment to ask OP to improve their question. In any case this post does not need moderator intervention. Close/down- vote should have sufficed. </li>
<li>Nov-4: <a href="https://biology.stackexchange.com/q/40260/3340">Please explain this disrepancy about ageing</a> <br> <strong>Flagging reason</strong>: "... this is just an attempt by a creationist to poke holes in evolutionary theory by what they presume is an inconsistency without actually knowing the finer details of the molecular processes involved or how they relate to organismal survival. For that reason this post should be closed." <br> <strong>Decline reason:</strong> I should have actually declined this for not finding an evidence in support of the flag. However, you claim that OP is basing their question on creationist beliefs. This you also commented to which OP has replied that they are not citing the Bible or any other religious book. This flag was unnecessary. Again, you should have voted to close or downvoted if you think background research is not done. </li>
<li>Nov-16: <a href="https://biology.stackexchange.com/q/40671/3340">https://biology.stackexchange.com/q/40671/3340</a> <br> <strong>Flagging reason:</strong> VLQ <br> <strong>Decline reason:</strong> Same as in case 2</li>
</ol>

<p>Some of the flags have not been declined by me (in case if you are assuming that I am the evil despot here.)</p>

<hr>

<p>Regarding AliceD comment: <em>It may be me, but you have been mod-closing many questions - you shouldn't bring up a (very valid) argument that you are not practicing. Further, AMR's argument goes beyond this specific case.</em></p>

<p>When I close questions, I close them for their content, after reading the posts. Most closures have been for duplicates or very broad. These are the times actually when I wish I do not have a binding vote. Anyway, I shall try to limit myself to just post comments when I feel a certain post deserves closure for scientific content. Flags, however, are a different matter. Moderator is not supposed to verify the scientific authenticity of the content. If AMR's argument goes beyond this specific case then it is expected that they explicitly point out at least a few instances when their flags have been unjustly declined. </p>

<hr>

<p><strong>Addendum</strong></p>

<p>I was unaware that you could not cast a close vote. However, when you think a question should be closed then you can flag the question for closure. These flags are dealt by the community. Moderator attention flags are to be used only in very specific situations. Yes, migration is a valid reason but it is good to wait for the community's verdict on whether the question is really off-topic. I would suggest that such questions be VTCed as off-topic with a custom reason saying that it belongs to another site. But as such there is no harm in calling for mod attention for migration when you are sure enough. The flag may be rejected, though. Better to comment first and ask OP for clarification in doubtful cases.</p>
 1306: <p>I am not a mod here so I don't have access to your flagging history. However, based on the public data from your profile, we can see that:</p>

<ol>
<li><p>You have raised a total of <a href="https://biology.stackexchange.com/users/16651/amr?tab=topactivity">91 helpful flags</a>;</p></li>
<li><p>You have cast a measly <a href="https://biology.stackexchange.com/users/16651/amr?tab=topactivity">14 downvotes</a>.</p></li>
</ol>

<p>Based on that and on the <a href="http://chat.stackexchange.com/rooms/1997/conversation/flagging">discussion</a> we had about this in the chat room, you seem to feel that flags are the first line of defense for the site. They aren't. The first line of defense is voting. That's precisely why downvoting questions carries no rep penalty and why the first reason given for downvoting is lack of research:</p>

<p><a href="https://i.stack.imgur.com/pJ14W.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/pJ14W.png" alt="downvote popup"></a></p>

<p>In your case, since you don't have the rep to close vote directly, flagging for closure is perfectly OK. However, you should really try to avoid using the custom mod flag unless none of the other reasons apply. </p>

<p>So, of the 5 flags cited by WYSIWYG, I would also have rejected 1 and 3. In the case of 1, lack of research is no reason to flag, it's a reason to <em>downvote</em>. Raising flags on posts that don't actually need moderator intervention is just creating work for the moderators for no reason. Just downvote and move on. If you must, flag to close as homework but don't flag for mod attention. What was the mod supposed to do? We try to avoid unilaterally closing questions since mod votes are binding. It is far better to let the community decide unless the question is an egregious example, completely off topic or whatever. </p>

<p>Your 3rd flag was because, in your opinion, the question was from a creationist. That is no reason to flag at all! First off, we have not made creationism or ID explicitly off topic. It is not mentioned anywhere in the help center. There have been some meta discussions (<a href="https://biology.meta.stackexchange.com/q/111/1306">1</a>,<a href="https://biology.meta.stackexchange.com/q/84/1306">2</a>, <a href="https://biology.meta.stackexchange.com/q/732/1306">3</a>) on the subject but none has had enough votes to reach a consensus and, in any case, it hasn't been made official, so it isn't a valid reason to close, let alone flag. </p>

<p>I should also point out that the golden rule for migrating questions is <strong><a href="https://meta.stackexchange.com/a/91446/203101">don't migrate crap</a>.</strong> I don't have the rep to read the deleted question you mention but if it was both off topic here <em>and</em> a bad question, then it shouldn't be migrated and the mods were right to decline your flag. We can't use other sites as our dumping ground just like we wouldn't like to receive crap questions from elsewhere. Therefore, that the question was eventually deleted is no indication that your flag was valid. </p>

<p>In conclusion, please try and only flag what needs to be flagged. Your first choice for bad questions should always be a downvote and flagging should only be a last resort. </p>
