Well, I assume we need to do this: https://docs.flathub.org/docs/for-app-authors/submission#someone-else-has-put-my-app-on-flathubwhat-do-i-do
Then make me, and a few other people as maintainers, at least someone else (just in case I go evil someone can stop me).
I would then make sure I understand how the flatpak works, fix the OP's errors, and then we just need flatpak verified.
https://docs.flathub.org/docs/for-app-authors/verification
Then we'd be good.
We can mark flatpak as not as high supported as binaries, just getting it verified would be nice.