Brawler here.
VS All brawlers.
Charizard tends to be easily caught up in brawler's combos and has significant issues landing. Brawler will not have any issues punishing Charizard either, and playing the footsies game with him causes victory. Hard matchup for Charizard, as he won't be able to keep up with brawler. The range/disjointed moves Charizard has is his best hope.
VS 2122 or 2132
He is easily caught in helicopter kick or piston punch, but can also punish feint jump harder than most other characters with OOS usmash.
VS 1111
Charizard is slow and big enough to get hit a bunch by shotput, and will have a hard time weaving around them. His recovery is also easily challenged by head on assault, which will result in Charizard's death. Nevermind, tested this. It can challenge fly near the end, but not flare blitz. It's also difficult to challenge fly. The only thing charizard needs to watch out for when facing 1111 brawler while recovering is rar down b if he's near the outside of the ledge.
All in all- I think brawler wins the matchup, but brawlers who don't know the matchup will struggle due to Charizard's range and disjoint.