If you're looking for vintage shops you should head over to via del governo vecchio and take a walk around rione monti (esp. via panisperna and via dei serpenti). There are quite a few around trastevere, but i can't be specific here, you'd have to walk around!
The biggest flea market in the city (and quite possibly the only one) is Porta Portese. They also have a monthly flea / vintage / emerging designers market in Rione Monti, it's a weekend a mont or even more at times. that's cool and less chaotic than porta portese which is quite overwhelming
