Hyper Voice was learned via breeding (source). I supposed if a male and female both have it from the earlier generation that babies in Kalos FROM THOSE TWO EEVEE (or their evolutions) can learn it. Same principle as being able to learn any moves from the parents from the normal moveset. However, this would require experimentation on my part. Thankfully, I can hack and thus clone the shards needed to teach two Eevee the move, then clone and import them, so I can test it easily should I do this experiment.
For now, looking into a 5IV Vullaby with Steel Wing. I found an existing contact to pop the Egg for me and gave him a 5IV Meowth for it. Now I have to train it to the point breeding won't cost me too much (forget the fact I got 400,000+ PokéDollars in the Battle Shateau last nite and a few Pay Days from Meowth can often cover the tab from Lv.20 or so onwards).
I took a Shiny Charm step last nite by importing a batch of babies, over half of which I bred in Black for import. I didn't feel like fishing yet, so bred some fishing ones too. Also covered the rest of the starters and, of course, the Vullaby that started my experiment. So I can do some evolving work now. Being able to buy Leaf, Water, and Fire Stones (why not the rest? We have 5 or 6 each for Sun and Moon...though they are via Pickup 10% rate each eventually) is very handy, too, as I can now evolve a Pansage trio without worrying about their movesets (not like I plan to use them for anything other than Egg breeding anyway with Egg Moves).