Unfortunately most anticheats does not allow loading untrusted dll in game. But It's on plan to release code signed library.
If Flutter provides an interface to render on offscreen texture, integrating with it shouldn't be that hard.
I did end up looking into it a bit. One would have to build a new Embedder Engine for Flutter, which they provide examples for. But the implementation is significant. Probably achievable for a small team.
I was thinking into apply this overlay on cs2, but I'm really afraid of VAC ban. Maybe try to hook on another know application as discord overlay or steam overlay itself?