I agree that you need an ignition source and this may not be likely, I'm just not confident its unlikely enough! As I recall the energy needed for ignition is also lower in high O2 conditions.
Interesting link
here about chamber treatment/fires; a few excerpts:
"Fire under hyperbaric conditions is always more intense because there is more oxygen available to support combustion. A rise from 21% to 28% in the oxygen percentage will double the burning rate. As the pressure is increased, the amount of oxygen available to burn increases. The increase is equal to the percentage of oxygen available multiplied by the number of atmospheres in absolute terms. For example, at a pressure of 4 ATA (equal to 30 m of sea water), the effective oxygen percentage would be 84% in compressed-air. However, it must be remembered that even though burning is very much accelerated under such conditions, it is not the same as the speed of burning in 84% oxygen at one atmosphere. The reason for this is that the nitrogen present in the atmosphere has a certain quenching effect."
"In monoplace chambers pressurized with 100% oxygen, a fire will be instantly fatal to any occupant. The human body itself supports combustion in 100% oxygen, especially at pressure. For this reason, plain cotton clothing is worn by the patient in the monoplace chamber to avoid static sparks which could be produced by synthetic materials. There is no need to fireproof this clothing, however, as if a fire should occur, the clothing would afford no protection. The only method for avoiding fires in the monoplace oxygen-filled chamber is to completely avoid any source of ignition."