If you chose either Squirtle or Bulbasaur as your starter in Red, Bubble or Vine Whip will annihilate Brock's Pokémon.
If you chose Charmander however, and choose not to abuse items or overlevel, the majority of Pokémon available at this stage of the game comprise of moves that Rock types resist, such as Flying, Poison, and mostly Normal. Fortunately, it's worth noting that Brock's Team has a poor movepool too - Geodude only gets Tackle and Defense Curl, when the latter isn't meaningful when most of your Physical moves won't deal much damage to it anyways. Onix meanwhile gets Tackle, Screech, which you can easily switch out from, and Bide, which can be abused quite effectively. This allows you to freely use any Pokémon that would otherwise be weak to Rock moves, as they would be in Fr/Lg. Regardless, here are a few Pokémon I would suggest to use:
Charmander - Though an obvious pick, Charmander's STAB Ember works off Geodude and Onix's far lower Special stat, allowing it to deal more damage than most other Pokémon. It's likely your highest-leveled Pokémon at this stage of the game too.
Nidoran-M - Horn Attack is the strongest BP move at this point of the game, accessible at Level 8. Nidoran's Leer can lower Onix's Defense without much opposition, though it's not as effective on Geodude. Nidoran-M also gets Poison Sting at Level 14, which can attempt to fish out Poison. Nidoran-M is preferred over Nidoran-F, as the latter gets Scratch, not Horn Attack.
Butterfree - If you really want to use a Butterfree, although it's not very good after this gym, it gets Confusion at Level 12, which is a Special move Rock/Ground types do not resist. Therefore, it tears through the Rock Gym like no other Pokémon, besides the other two starters.
Beyond abusing inaccuracy with Pidgey's Sand Attack or possibly using Weedle's Poison Sting in an attempt to Poison the opponent's Pokémon, these are likely the only Pokémon worth using for Brock. These recommendations should get you past your first true obstacle in a Pokémon game, and uh, please don't kill me.