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.

What he means is, "Okay, seriously, Mercutio, let's get out of here. It's so hot, and our enemies the Capulets are hanging around nearby, and if we run into them, there's no way we can avoid getting into a fight with them. It's because it's so hot outside that it makes people get irritated easily and want to start fights with each other."

Benvolio's words here are foreshadowing the terrible way this scene will end. As you can see, he often tries to be a peacemaker, or at least keep his friends out of trouble. But after he says this to Mercutio, the two of them just playfully bicker for a while, not heading inside, and then the Capulets do show up. Romeo does, too, and a brawl does break out--and Mercutio dies.