Android

To add a launch screen (also known as “splash screen”) to your
Flutter application, navigate to .../android/app/src/main.
In res/drawable/launch_background.xml,
use this layer list drawable XML to customize
the look of your launch screen. The existing template provides
an example of adding an image to the middle of a white splash
screen in commented code. You can uncomment it or use other
drawables to achieve the intended effect.

For more details, see
Adding a splash screen to your Android app.

iOS

You can also fully customize your launch screen storyboard
in Xcode by opening .../ios/Runner.xcworkspace.
Navigate to Runner/Runner in the Project Navigator and
drop in images by opening Assets.xcassets or do any
customization using the Interface Builder in
LaunchScreen.storyboard.

For more details, see
Adding a splash screen to your iOS app.