Even if you build the splash screen if Flutter, you still need to set one in via XCode. Otherwise, the app loads with a momentary plan white screen and Apple rejects it.
If you want to extend the time till the moment data process is over, then you will have to make a replica of LaunchScreen.storyboard in Flutter. The data processing and logic are written in Flutter. There's no way it can tell LaunchScreen.storyboard "I am done". What you can do is though, make a splash screen in Flutter which will look like LaunchScreen.storyboard. And once the data processing is done, you can navigate the user to the desired screen. Since the two screens are same, use won't see the difference and the app will smoothly show the next screen.
Just a word of caution - be careful about extending the timing of launch screen. Apple may reject the app. See if something can be done after the screen load. You can use flutter after layout package for this or the below line will do the trick :
WidgetsBinding.instance
.addPostFrameCallback((_) => myFunction(context));
This thread may help you to delay the screen for XX seconds.