Champion Chests (25 cost per reroll) are the best way to use rerolls for Mythic Parts
Legendary Chest have a higher probability of rerolling Mythics (20% vs 15%), however their much higher cost of rerolling (50 vs 25) makes it less optimal
Epic Chests cost less to reroll (10 vs 25), but the lower cost does not justify the much lower probability of Mythic Parts (3% vs 15%)
Common(1), Uncommon(2) and Rare(4) chests are not known to provide Mythic Parts