There are 5 HMs in XY: Cut, Strength, Surf, Fly, and Waterfall. Fly is easy enough to allocate to a non-slave Pokémon so that leaves Cut, Strength, Surf, and Waterfall. Guess what Pokémon can learn all of these moves?
Yes, Bibarel. The same go-to HM slave as Gen 4. It can learn all four of the above HMs, and gets STAB from them as well, making it not 100% useless in combat. Be sure to give it an awesome nickname like "God" or "Chuck."