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It seems to be a bug with GB Studio 2 beta, since GB Studio 1 doesn't have the flashing issue. If the issue gets fixed in later updates, I'll reupload a new build of the game.
I could've made it that the text boxes would slide down with every new message shown, but it would take more time, and there's a lot of characters that talk, haha.

I think in games like Pokémon they would keep the box up but just clear it whenever there's a new paragraph?

Might be a solution.