First and foremost, meet the intent of the rules. This being Lemons, they can take their ball and make you go home if they want.
Having performed flammability testing on a lot of materials for my job, I will never tell someone not to worry about flammable materials in a safety critical environment. Having said that, I wouldn't worry about any padding in the seat pan or lumbar area. There is no ignition source if my butt is in the seat covering it, and I don't care what happens to it once I exit the car.
I would worry most about the cover. If it won't burn, it will take quite a while for any padding underneath to ignite. Then I'd worry about the padding in the bolsters where there's only the cover between any fire and the padding. Crap under my butt will never get hot enough to ignite as long as my butt's in the way. (Although I may reconsider how hot the seat padding is when I'm on the track wearing my padded quilt of a racing suit.)