What does 'scape a brawl' mean in Act 3?
It means "escape a brawl," or in other words, "avoid getting into a physical fight."
A brawl is a noisy, chaotic fight, the kind that we expect the Capulets and the Montagues to get into. It won't be just one-on-one--it'll involve lots of Capulets against lots of Montagues, and that's going to get messy and painful, possibly causing injuries or deaths, and it might get them in trouble with the law, too.
This phrase appears in the very beginning of Act 3, Scene 1, as Benvolio and Mercutio are hanging out together outdoors. Here's what Benvolio says:
I pray thee, good Mercutio, let's retire.The day is hot; the Capulets, abroad;And if we meet we shall not 'scape a brawl,For now, these hot days, is the mad blood stirring.