Are you 'sure' it's paint ?
I have a set of aluminium pots that were use on birch fires. Tar burns on black and blacker yet over the years on these. Mine were used as dye baths and simmered for hours.
The thing is though that once the surface soot has been washed off then the black is stable. It's like the coating on old chip pans, which got thick and crusty and didn't go on fire or flake off. The only way to remove that was either elbow grease and brillo pads or to soak for 24 hours in washing soda. Folks just didn't bother, but emptied out the old dripping, cleaned the pot, added fresh blocks and cooked again.
My old dyebaths are definitely not smoothly coated, but the black isn't a problem.
M