The first place to consult if you want to use animations in your apps is the official Flutter guide, which you can find at the following link: https://flutter.dev/docs/development/ui/animations. Another great resource with videos, examples, and step-by-step guides is https://buildflutter.com/functional-programming-with-flutter/.
In this chapter, we've built a game starting from scratch. This is probably not the most common scenario for a real-world game, as there are several libraries and toolkits that you can leverage to create complex apps and games. If you are serious about creating compelling animations, there's a third-party tool, called Rive, that allows you to create incredible animations and add them to your Flutter apps. More on this can be found at https://rive.app/.
There's a great example on how to build a multi-platform game with Flutter...
