Flutter is a cross-platform framework like Xamarin. You use it if you want to develop apps that work on both Android and iOS. If you want to target only Android, there's no real point to using Flutter.
If you do want to use a framework like Flutter, you have no choice in programming language. Flutter uses Dart, and Xamarin uses C#.
Making a lot of money through apps is probably impossible if you're working on your own. It is certainly possible, although not guaranteed, for a big team. It is possible to make some money if you are working on your own, but it's not assured that it will provide a better income than doing something else in that time.
The choice of language or framework is irrelevant to the question of making money.
does flutter can build app (android) faster than native (java / kotlin)?
Probably not. As Stephan said, its point is cross-platform compatibility, not development speed. Kotlin is the popular choice for Android development these days - people who use it seem to like it better than Java. Plus, since not many people use Dart, there are a lot more ready-made libraries to use with Java/Kotlin than with Flutter.
One reason I never took a job building Android apps was that the local recruiters weren't offering salaries that were anywhere near what I could make doing things like web applications. In fact, less than half.
Part of this is the same sort of exploitative environment that game companies are infamous for, but a lot of it has to do with the fact that people expect their mobile apps to be free or nearly so - generally under USD $5 or adware-supported. So unless you develop a really popular app like Flappy Bird, you won't have enough customers to make a decent living unless you're located in an inexpensive country.
I've never programmed Android in anything but Java, but Kotlin is quite popular and if Oracle's legal department manages to do to Java what they want to do, Kotlin might be a good choice as an "Oracle-proof" code base.
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