To me, There are four ways to beat Brock in Pokemon yellow.
1. Catch a Mankey and train it until it learns Low Kick.
2. Catch a Caterpie, train it until it evolves and learns Confusion
3. Catch a Weedle, train until it evolves into Beedrill
4. Catch at least 3 Pidgeys, train them all until they learn Sand Attack.