If this is a fire breahing dragon, I imagine food wouldn't rot in the mouth, avoiding dog-breath. They'd be scorching the organic material to ash every time they take a flamey. As others have pointed out, the chemicals which start the fire could probably play into the smell, but I always imagined they smell like electricity on a wet day. Like static on a VCR, like old lamps. Like solder (hot lead and tin or whatever it is. That sweet, metal tang). I'd go for a subtle, quite pleasant smell with a hint of danger. One of my earliest tries at a story included dragons. Their scales were made of iron, and as they approached the end of their natural life, they'd start to rust, slowly exposing the flesh underneath. As one might imagine, most dragons opted to die in combat at a more reasonable age. Uh, anyway, during this process, they would reek of strong acids, and you wouldn't want to breath those fumes.
