How much damage did this do to the Brahma? How soon did you break up the conflict? Very often, a conflict between two chickens is quickly resolved if you just let them settle things between them.
Standing aside and allowing the two to have a skirmish is often the best way to promote peace in the flock. By constantly breaking up fights, you actually prolong the conflict, risking it continuing and becoming a "thing".
A fight that needs breaking up would be when an aggressive chicken is standing on the back of one pinned to the ground, pecking at her without signs of letting up, maybe even tearing flesh.
A normal argument over rank involves two chickens flapping wings, claws out, and sometimes one latching onto the other's comb. Sometimes a comb will bleed. Then the fight is over, usually in a matter of 30 seconds or less. This is very normal. The social order is constantly changing, mostly in ways you won't even notice.