Yes. When DFC except for the origins walkers flip they do not leave the battlefield and so are the same game object. Any auras, equipment, or counters on them will remain on them.
April 19, 2016 12:27 p.m.
says... Accepted answer #2
Unless the creature has left the battlefield and returned, or the creatures new flipped side has protection from a feature of the enchantment on it (In this case Curiosity), or if the enchantment can only enchant a specified type of permanent and the now transformed thing it is enchanting is no longer that type of permanent then it should retain the enchantment.