Question: do paladins get wings 5e?
Answer: Aarakocra have feathered wings, as do level 20 Vengeance Paladins. That said, there are other things with wings, like level 14 Draconic Sorcerers or Variant Winged Tieflings that you could reflavor as feathered, even though they're not. You could even learn the Fly spell and just say it gave you feathered wings.