Multiple ways you could do this, but the easiest one which I use is:
For Launch Icons I use the flutter library Flutter Launcher Icon
For the Custom Splash Screen I create different Screen resolutions and then add the splash images in the mipmap folder as per the resolution for Android.
The last part is adjusting the launch_background.xml in the drawable folder in res folder in Android.
Just change your code to look like below:
<?xml version="1.0" encoding="utf-8"?>
<!-- Modify this file to customize your launch splash screen -->
<layer-list xmlns:android="http://schemas.android.com/apk/res/android">
<!-- <item android:drawable="@android:color/white" />
<item android:drawable="@drawable/<splashfilename>" /> --> -->
<!-- You can insert your own image assets here -->
<item>
<bitmap
android:gravity="center"
android:src="@mipmap/<Your splash image name here as per the mipmap folder>"/>
</item>
</layer-list>
Few devs I have seen add the splash as drawable, I tried this but somehow the build fails in Flutter 1.0.0 and Dart SDK 2.0+. Therefore I prefer to add the splash in bitmap section.
iOS Splash-screen creation is rather simpler.
In the Runner folder in iOS just update the LaunchImage.png files with your custom Splash screen images with same names as LaunchImage.png @2x, @3x, @4x.
Just an addition I feel its good to have a 4x image as well in the LaunchImage.imageset. Just update your code in Content.json with following lines, below 3x scale to add a 4x scale option:
{
"idiom" : "universal",
"filename" : "[email protected]",
"scale" : "4x"
}