Class referenced in the manifest, io.flutter.app.FlutterApplication, was not found in the project or the libraries
That's normal because the Flutter SDK doesn't have code check for Android code. Even if there are warnings thrown from the Android code, you should still be able to run the Flutter app if the Android code doesn't have "real" errors.
What you can do here is to enable code completion for Java/Kotlin on Preferences > Language & Frameworks > Flutter > Experiments. This should remove the warnings thrown on the Android project even if the code is correct.
... or click on Tools > Flutter > Open Android module in Android Studio. This should open the Android build of the Flutter project on Android Studio and help check if the warnings given are correct.