Bane: not sure
Brainiac: not sure
I think FS wins both of these matchhups.
With Bane he really just controls the pace, has strong enough zoning to wind down trait when he has to, reaction mb b3 to charge, mix up whether or not you mb the trap, use trap as a trip guard if they try to jump in, etc. He just has good enough space control to make this matchup not super difficult imo. Rushdown is a bad idea because reversal armor just ruins Firestorm's plus setups a lot of the time, but just avoid this and you're good. Probably 6-4 for FS, you just stay defensive.
I would say we win Brainiac too but not as easily. Like we don't have a good AA to counter approach but if you read or react quick enough then psycho crusher takes out his tendril swing pretty easily, staying at midrange you can use trap to get rid of/blow up activation of trait pretty easily, better zoning again, and very comparable damage for the difficult Brainiac has getting in. All Brainiac can do is hope that you respect the mb divekick possibility and outfootsie you once you convince him to respect the air control, but it's not *too* hard to stay out of his range. FS can also go in and abuse his frames more easily on Brainiac than a character like Bane where reversal armor is a problem. Most of Brainiac's moves are slower. I would put this closer to 5-5 I think, but slightly in FS favor.