You cannot use GBA buttons to directly change the system's color output or palette. Here's why:
If you are the developer (writing homebrew / hacking ROM), you can program buttons to:
BLDCNT / BLDY / BLDALPHA registers.Summary: Buttons → Game Logic → Palette Change (if programmed). Buttons ↛ Hardware Palette. For playing existing games: Impossible. For making games: Standard practice.