Try using an Electric-type Pokémon, like Eelektross, of even an Emolga. Electric-type Pokémon resist Flying-type attacks. Rock also resists Flying, but, since this is Skarmory We are talking about, DO NOT use a Rock-type Pokémon. Steel resists Flying as well. A perfect example of one that can also take down that Skarmory is Klang/Klinklang.
Note that these Pokémon I mentioned can learn Electric-type attacks, so it'll be easier to destroy Skarmory.
Good Luck, fellow Trainer.