What happens to an Aura attached to a permanent that is flickered with Ephemerate?

When a permanent is "flickered" by Ephemerate, it is exiled and then immediately returned to the battlefield. Under CR 400.7, a permanent that leaves and returns to the battlefield is treated as a brand-new object with no memory of its previous existence. The Aura that was attached to the old object has no automatic connection to the new one.

When the enchanted permanent leaves the battlefield (even briefly), the Aura it was enchanting loses its legal target or object to be attached to. Under CR 704.5m, the game's state-based actions check for Auras that are not attached to anything — or are attached to an illegal object — and put them into the graveyard. This check happens as soon as the permanent is exiled, before it returns.

The returning permanent comes back as a new object, completely unenchanted. The Aura does not "follow" it back, because the new permanent is a different game object and the Aura is already in the graveyard by the time the permanent returns.

Example: You control a Grizzly Bears enchanted with Ancestral Mask. You cast Ephemerate targeting Grizzly Bears. Grizzly Bears is exiled — at this point, Ancestral Mask has no legal permanent to be attached to, so state-based actions put it into the graveyard. Grizzly Bears then returns to the battlefield as a 2/2 with no Aura attached.

Note: If the Aura's controller wants to keep it, they would need some other effect that moves the Aura or re-attaches it. Simply flickering the enchanted permanent will always cause the attached Aura to be put into the graveyard (CR 704.5m, CR 400.7).