Sky Drop does no damage to Flying-type Pokémon, but it will still pick them up (making them unable to move) on its first turn.
Sky Drop will fail if the target is behind a substitute, or if used on a target that is already semi-invulnerable due to moves such as Fly, Bounce, or another Sky Drop.
Air balloon and levitate weren't mentioned, I think you can find out on showdown, however it is still beta so it might be wrong
Source: https://bulbapedia.bulbagarden.net/wiki/Sky_Drop_(move)
This is for gen 5, gen 6-7 didn't mention anything, except for
Targets weighing 440.9 lbs. (200 kg) or more cannot be lifted by Sky Drop, causing the move to fail.
According to https://pokemondb.net/move/sky-drop
Sky Drop will appear to work on Flying-types and those under the effects of Levitate, Magnet Rise or Telekinesis, but will not cause them any damage
