If you're taking shingles, chances are you don't have a true flat roof (or just a terribly built one), since those are supposed to continuous roofing in order to withstand water puddles. Back in the day the only material available was asphalt tar, which obviously isn't very fireproof. Modern alternatives such as EPDM and TPO though are plenty fireproof, especially if placed on top of polyisocyanurate insulation (which doesn't burn, only char) instead of directly on the wood deck.
Sorry for my lack of clarity, I was talking about both types of roofs, since the classic Somerville triple decker has a flat roof, and the classic Philadelphia a pitched roof with shingles. I was wondering about the former since I've never seen one as such, aside from some one story commercial ones when I lived in a higher adjacent apartment.
And thanks for the comments, you've saved me some research when it comes time to replace my roof.
