Aerie Ouphes' persist ability triggers, returning it from your graveyard to the battlefield.
Aerie Ouphes enters the battlefield, triggering Denry Klin, putting at least one +1/+1 counter on Aerie Ouphes.
Resolve the Aerie Ouphes ability, dealing damage equal to its power to Swans of Bryn Argoll, causing you to draw cards equal to the damage prevented this way.