American-flag fish (note that the name is for the American flag - not for a flag fish that is from America if you get what I mean - many people get this mixed up) are killifish but have behaviours similar to both cichlids and gouramies. IME, they are relatively peaceful though some can be nippy and males do become especialy aggressive during breeding times and are territorial. I suspect the problem you are having with the bala has more to do with the circumstances than the fish itself. You may or may not be aware that balas get to 12" and require a tank of at least 125 gallons. If your tank was this size and the American-flag fish was chasing your bala around I would then suspect the problem to be that balas are very skittish schooling fish so a lone bala is an easy target for a relatively boisterous, though small, tankmate. If your tank is large enough (at least 100 gallons), you could add a couple more balas and this should solve your problem. If the tank is smaller, the bala shouldn't be in there in the first place and the tank size is likely the cause for your problem.
Oh and there is a flag cichlid but I am pretty sure this thread reffers to the killifish as the red and blue markings are very characteristic - especialy of the brighter males.