To go through the mill means to be abused or treated very harshly, and in this example a work of literature is being treated harshly by vanity publishing.
Consider the statement "I told her almost everything, including my reticence about seeing this work of literature be abused and treated in an extremely harsh manner which was vanity publishing.". Is the statement "I told her almost everything, including my reticence about seeing this work of literature go through the mill which was vanity publishing." false? Yes/no/unknown