My understanding on how it works is that, in order to get an Alolan Vulpix, one of the breeding parents must already be an Alolan Vulpix. So, for example, if you were breeding a standard Vulpix with an Alolan Vulpix, you'd have a 50/50 at getting either form as offspring.
So, if you're playing Moon, you'll need to trade to get an Alolan Vulpix.