It seem to give you the martial flexability class feature but the wording is a little unclear. So would you allow it? Would raw allow it?
No. Barroom Brawler dont give you the 'Martial Flexibility' class feature. It gives something similar .. not more. So you dont qualify for 'Extra Martial Flexibility'.
Prerequisite(s): Martial flexibility class feature.
You have learned how to mimic the combat tricks and forms of others.
Prerequisite(s): Base attack bonus +4.
Benefit: Once per day as a move action, you can gain the benefit of a combat feat that you do not possess for 1 minute. You must otherwise meet the feat's requirements.
Special: If you have the martial flexibility class feature, this feat instead grants you one additional use per day of that ability.