Almost every common modern FR4 PC board I can remember has had some sort of UL94 rating (there are levels). And doesn't UL94 apply to plastic parts only? I'm not an expert in this subject, but I believe it is targeted at plastic parts used on products. I don't know if it would apply to the completed product, unless it was enclosed in plastic maybe? The term I used to hear was non-self sustaining fire or self extinguishing fire.
There are a few components that have plastic parts on a full size Pi.. the GPIO connector, HDMI, USB and microUSB, ethernet, camera and display connectors. I would expect all of these components to be made of some level of UL94 material. Although anything is possible and some might not be UL94 rated per se.. but I would guess that it would be difficult to find these parts made with flammable plastics, especially from a known vendor as the RPF would use. I can't see much else on a Pi board that would sustain any sort of fire.
Power problems? MoPower UPS for the Pi