"Never drink in a pub with a flat roof."
British proverb
A flat roof pub is exactly what it sounds like -- a pub that was constructed with a flat roof. The subtext here is that these pubs were built in the 60s or 70s, and are often the result of urban sprawl or appear on the edge of housing estates (or, as Americans would say, a housing development). They are sometimes converted from older shops. The upshot of this is that they are newer (but not brand-new), and they are drinking establishments of convenience, somewhere you don't have to travel far to get to.
However, the stereotype goes deeper than this -- flat roof pubs are, in the popular mind, the hangout of the lower classes, who are there to get drunk, get in fights, and maybe engage in something illegal. This is where you go to hang out with Britain Firsters, watch a dog fight, and get in a fist fight for lack of anything more productive to do.
Of course, this is a stereotype, and it isn't actually a very good rule of thumb. There are many fine old pubs that have a flat roof and are quite classy. Moreover, 'flat-roof' means different things to different people, and may refer to something akin to an American dive bar (or worse), or to simply a modern 'strip-mall' bar with no personality.