Yeah, the different fonts do work pretty well. Although part of that is making sure the font is a good stylistic match for the language - black letter for Gothic, etc. (and then there's Ptenisnet the Egyptian, speaking only in hieroglyphics)
i think the im gay bubble is more readable than the other flags in the OP would be, because in the im gay bubble the flag pattern blends more with itself (less visually busy) while still clearly being a flag.
I like the flags in the bubble idea, but I'm also worried about them not coming through. Maybe put little flags next to the bubble? Like... sometimes Fruits Basket uses little symbols to show who's talking if they're not on the page (like a flower for Hanajima...) so something like that? That might be similar to what @Kaylotta was saying?