Go heal up at the pokécenter. Now that you have defeated Elder Li in Sprout Tower, you can go up the elevator in the Violet Gym. The Gym Leader, Falkner, specializes in Flying pokémon.
The pokémon that you will encounter here are all dual-typed: Normal/Flying. As such, they are weak against Rock, Electric, and Ice moves, strong against Bug and Grass moves, and are completely immune to Ground and Ghost moves.
The first trainer you encounter has a Level 9 Spearow. It is going to know normal and flying moves, so you don't want to bring Fight, Bug, or Grass-type pokémon against it. The types that are strong against flying moves are Rock, Steel, and Electric.
Because of this, you can use your starter unless it's Chikorita, although none of the starters will know rock, electric, or ice moves yet, unless you have Totodile and have been leveling him up like crazy.
If you traded a bellsprout for an Onix in town, that's a good pokémon to use in this gym. Also, you could go catch a Geodude in Route 46. Also, if you want to, you can go south of Violet City and try to catch a Mareep in the grass. It's an electric type pokémon, so it would be another great choice to bring here.
The other trainer has two level 7 Pidgeys, who also know only normal and flying attacks. These also might know Sand-Attack, which lowers accuracy. This can be a problem if your pokémon's accuracy gets really low, because the battle will drag on as it struggles to land a hit. Lowered accuracy can be cured by switching the pokémon out, so try that if you're having trouble.
Finally, Falkner has a level 9 Pidgey and a level 13 Pidgeotto. The Pidgeotto knows Roost, which increases its HP by 50% of its maximum HP. This can make the battle take a while, especially if you don't have any strong moves to bring against it. But if you have a Mareep who has the Static ability, you have a chance of paralyzing Pidgeotto whenever you tackle it, which can make it harder for it to use Roost.
Tips for Defeating Falkner
- Bring Rock, Steel, or Electric pokémon if you have any.
- DON'T bring fight, bug, or grass-type pokémon.
- Use Rock, Electric, and Ice moves if you have any.
- DON'T use bug, grass, ground, or ghost moves.
With a little bit of effort, you will defeat Falkner to win your very first Gym Badge, the Zephyr Badge! With the Zephyr Badge, pokémon up to level 20 will always obey you, and also, you can use Rock Smash outside of battle. Falkner will also give you TM51, which contains Roost.