Strong Against Flying Type
Electric, Rock and Ice Type have the Super Effective rating against Flying Type Pokemon. Use Electric Type attacks like Thunderbolt, which not only causes massive damage to Flying Types, but also has a chance to cause paralysis. All Rock Type attacks are strong against Flying Types, but the Smack Down attack causes Flying Types to be weak against Ground Type Attacks as well. Ice Type Attacks that also cause freezing, like Ice Beam, offer the best strategy.
Weak Against Flying Type
Other Pokemon in your team may be at a disadvantage to Flying Pokemon. Ground Type attacks will not inflict any damage against a Flying Pokemon, unless the Flying Pokemon has been afflicted by Smack Down. Flying Pokemon also have strong defenses against Bug Type, Grass Type and Fighting Type attacks. Likewise, Flying Type attacks do a large amount of damage against Bug, Grass and Fighting Type Pokemon, so it is best to switch these Pokemon out when confronted by Flying Type Pokemon.
Normal Type Attacks
If your current party does not have a type of Pokemon that is strong against Flying Type, you can still defeat it using other strategies. Flying Type Pokemon take the base amount of damage from Normal Attacks, such as Doubleslap and Barrage. If you have a high level Pokemon with Normal Type attacks it will still be effective against the Flying Pokemon. Normal Type status attacks, such as Glare and Lovely Kiss, also effect Flying Types.
Dual Type Pokemon
Flying Type is always the secondary Pokemon type, except for the Pokemon Tornadus. This means all other Flying Type Pokemon have additional weaknesses based on their elemental type. For example, the Flying Pokemon Crobat is also a Poison Type, which means it is weak against Psychic Type attacks. Use this to your advantage when applicable, but keep in mind that Flying Types are always immune to Ground Type attacks, even if their primary elemental type is usually weak to Ground Type attacks.