You can use Visual Studio Code to develop the Flutter UI module in Dart and Visual Studio to develop the Xamarin backend written in C# .
Can I use C++ in Flutter?
I would take a look at Platform Channels, which are a way to communicate Flutter code to platform native code (e.g. Java/Kotlin on Android, Objective C/Swift in iOS). From there, you can use your C++ library using the regular NDK mechanisms .