The types of pokémon that you will encounter in this gym are Normal/Flying, Psychic/Flying, and Water/Flying. Against the Normal/Flying pokémon, Steel and Rock pokémon have both the best defenses and attacks. Against the Psychic/Flying pokémon, Dark type pokémon are recommended for their immunity to Psychic attacks. For the Water/Flying pokémon, they are super-weak to Electric moves (even weaker to it than they are to Rock moves), so Steel and Electric pokémon would work well against them.
The party that I brought with me consisted of Ferroseed, Zoroark, Boldore, Liepard, Krokorok, and Klink.
The highest level pokémon that you will encounter is L35, so I recommend training up your pokémon to at least that level before challenging this gym.
Getting through the Gym Puzzle
Skyla's Gym features cannons that you have to walk into and be shot out of in order to get around the gym. Be sure to look for the small arrow on the floor pointing at the cannon. You need to stand on this and walk toward the cannon in order to get inside. Use trial and error to figure out how to get through the gym. You might in some cases need to walk into the same cannon that you were just in, but from a different direction, in order to proceed. Try getting into each cannon from every possible direction.
Strategy for the Trainers
The first trainer whom you encounter is Worker Cliff, who has two L32 Tranquills. These are weak to Rock, Ice, and Electric moves. I used Boldore against them.
Next up is Worker Brady, who has an L32 Ducklett and Woobat. The Ducklett is super-weak to Electric moves, so use those. I used a Klink against it. As for Woobat, it is weak to Dark moves. I used Zoroark, but Liepard and Krokorok could also work well.
After that, you encounter Pilot Ted, who has an L32 Ducklett and Sigilyph. As before, use Electric moves on Ducklett. For Sigilyph, it is weak to Dark moves like Woobat, so I used Zoroark, but Liepard and Krokorok could work.
Next is Pilot Chase, who has an L33 Unfezant. It has the same weaknesses as Tranquill. As with Tranquill, I used Boldore.
The last trainer here is Worker Arnold, who has an L33 Swoobat. It has the same weaknesses as Woobat and Sigilyph, so I used Zoroark. Again, Liepard and Krokorok could be a good alternate choice.
Skyla's first pokémon is an L33 Swoobat that knows Amnesia, Heart Stamp, Acrobatics, Assurance. Use a Dark type pokémon and attack with Dark moves. I used Zoroark.
Next, Skyla uses an L33 Unfezant that knows Quick Attack, Razor Wind, Air Slash, and Leer. A Rock or Steel pokémon has good defenses against Unfezant. Rock moves are super-effective, as are Electric. I used Boldore. If you have Archen or Tirtouga, they could work well also.
Finally, Skyla sends out an L35 Swanna that knows Aqua Ring, Aerial Ace, Air Slash, and BubbleBeam. As with Ducklett, Swanna is super-weak to Electric moves. I used Klink.
When you defeat Skyla, you get the Jet Badge, which makes pokémon of L70 and lower obey you. She also gives you TM62 Acrobatics, which is stronger if a pokémon is not holding an item.
Now that you have defeated Skyla, you can go northeast on Route 7 and go to Twist Mountain.