iOS

In your Flutter project’s root directory,
navigate to .../ios/Runner. The
Assets.xcassets/AppIcon.appiconset directory already contains
placeholder images. Replace them with the appropriately
sized images as indicated by their filename as dictated by the
Apple Human Interface Guidelines.
Keep the original file names.

Updating the launch screen

Flutter also uses native platform mechanisms to draw
transitional launch screens to your Flutter app while the
Flutter framework loads. This launch screen persists until
Flutter renders the first frame of your application.

runApp() in the

window.render() in response to

window.onDrawFrame),
  the launch screen persists forever.

Android