if you are already expert on technologies you mentioned and know exactly how to work with them you might see investition to flutter as burden. Otherwise: Just go on with flutter & flame and see if it fullfills your requirements and could fit to your exact requirements.
Generally, flutter is already solid, and usable in context you mentioned. There's also plenty of resources to test if it would be ok to you before investing a lot. Just pick a demo project, get it running, and see results.
If you decide to invest you can take a working seed project generated to you
https://cli.vgv.dev/docs/templates/flame_game
Note: Flutter + Flame expect you to learn dart - it's easy, as the language is close to js / c / .. so: algol style syntax - it also expects you to understand reactive ui's - well: concept is insipired by React, so no suprises here, except that the whole concept needs some discipline.
Still to mention: For 3d games you still should see unity as solid option. And, as also with react native, you would find integration to flutter possible and supported by 3rd parties. Don't expect this to work always out of the box as a dream, but see it as a doable thing if you need to step to this road.
https://pub.dev/packages/flutter_unity_widget
As an inspiration I give you idea what kind of extensions Flutter offers, if you decide to invest on it.. This is more fun thing, but as a junior developer learning stuff and doing things out of interest this might be something to you.
If you're already deeply experienced with the technologies mentioned, diving into Flutter and Flame might initially feel like an unnecessary shift or even a step backward. But for those who are still exploring or looking to build something modern, lightweight, and scalable—especially for cross-platform projects—Flutter paired with Flame can be surprisingly powerful. I recently started experimenting with these tools for a small educational app based on [Historical Hijri calendars](https://tareekhijri.com/) and was impressed with the performance and flexibility.