Hmmm... Well, first, these special moves are all Egg moves. For example, you get a Poochyena with Fire, Thunder, or Ice Fang depending on your starter, and I've seen people finding Taillow with Boomburst and Skarmory with Whirlwind. The only thing I've seen in common is that these Pokemon were all found with the DexNav.
There isn't a known definitive chance for finding a certain Pokemon with an Egg move, but the chance increases as your DexNav level for that Pokemon increases. Your DexNav level for a Pokemon increases whenever you encounter that Pokemon, be it through a trainer battle or a wild battle.
Hope I helped!