Can't see any benefits on using nitrogen on my car's nitto tires. But aircraft tires are filled with nitrogen for safety reasons. Since nitrogen is inert, tires won't ignite or catch fire during heaving landing.
I believe the main reason for using nitrogen is to avoid the loss of pressure due to condensation/freezing of water vapor in the tires, which would definitely occur when flying at altitude.
As JS hinted, the tires can perfectly well catch on fire with atmospheric oxygen; whatever gas is inside won't have any appreciable effect until the tire blows out. At that point, the small amount of oxygen inside an air-filled tire wouldn't make much difference.
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