Sky Battle is the type of battle introduced in Generation VI. Sky Battle allows on the Type and Pokémon with Levitate to take part in battles. That is why Sky Trainer asks the player before battling.
Eligibility
As mentioned before, Sky Battle allows on the Type and Pokémon with Levitate to take part in battles.However there is an exception in case of Pokémon who are not flying in their natural sprite, like Starly or Pidove. Those Pokémon which can't fly such as Dodrio and Hawlucha are not able to take part in battle.
Gengar is the only Pokémon with Levitate not allowed to take part.