Yes, fire play is a form of BDSM. I've never done it but I guess it's akin to wax play which I quite enjoy. You don't actually burn the skin but the wax (or fire) creates a warm tingly sensation. It shouldn't be painful, although the skin may be irritated afterwards.
I think many people assume that people who engage in this kind of stuff are abusive and controlling. Yes, there's some dicks out there who watched Fifty Shades and have no clue what they're doing but most people in the BDSM community have a proper understanding of "Risk Aware Consensual Kink". Both parties need to give informed consent having discussed it at length and fully understood the risks.
The fact that your guy is talking to you about trust is the opposite of a red flag for me. It shows that he understands that you're certainly not going to blindly follow his lead without really trusting him. You'd quite literally be putting your life in his hands. And I note that he hasn't actually asked you to do it, just said it's something he likes...
If the idea doesn't float your boat, then just say so. Your body. Your choice. His reaction will tell you all you need to know. If he tries to push you to do something you've declined, walk away.
If you wanted to find out more about it, then you absolutely need to do your own homework. This looks like an informative article... freethoughtblogs.com/atg/2016/05/10/fun-things-to-try-in-kink-fire-play/
If it were me, I'd be asking a million questions about his experience to make sure he knew what he was doing. I'd also want to go and watch someone else do it first so I could see firsthand what was involved. I'd insist on having a third person, a spotter, present.
Tread carefully and keep yourself safe.