Can you share Domain colors with your teammate in Magma Chamber?

Yes — you and your teammate can freely run the same Domains (colors); nothing in Magma Chamber restricts that. The only 2v2 deck-building restrictions are that teammates can't use the same Champion Legend or the same Battlefields (CR 491.8.h–i), and Domain Identity is set individually by each player's own Champion Legend (CR 176.1), so overlapping colors are fine.

What you can't do is literally share the resources those colors produce. Each player has their own Rune Pool (CR 165–166), control isn't shared (CR 491.8.c), and you can't pay a cost with your teammate's energy or power — so a spell they invite you to play on their turn still comes out of your own pool, not theirs.