The move tutor in the Colosseum Marketplace teaches Fake Out to Raichu (Alolan) for $35,000 or 50 BP. You reach the Battle Colosseum after the Arc Badge.
One breeding gets Fake Out onto Raichu (Alolan).
Skitty
Pichu
Catch a male
Skitty. It has Fake Out from level 1. If it does not know it, the Move Reminder in the Colosseum Marketplace teaches it for a Heart Scale or $20,000.