With respect, get thee some #0000 steel wool and light a match to it. Blow on it gently & make a nice hot "coal"
It is the steel, sir, that is burning.
Some amount of carbon is necessary to harden the steel so the flint scrapes off a hot curly (frizzy, you might even say) which catches fire & burns.
A stainless steel flintlock would, I believe, be a very, very safe weapon.