I choose natural fabrics as much as I can for all of my general wear. I consider the risk of being involved in a fire while flying to be slightly greater than other things in life, but not so much so that I don't bother to consider the risk for many other activities too. Many thinks in life can put you at risk of fire, so I like to dress with that in consideration.
With the exception of specialized flame proof fabrics, most any of the rest will burn to some extent. For me the important factors are: Will it melt and stick to me while burning, and become fuel I cannot remove while burning? And if it is burning, will "stop drop and roll" likely extinguish or at least subdue it?
In a cockpit, stop drop and roll has limited potential as a fire management tactic, so that leaves me with "can I remove it while burning?", which takes me back to natural fabrics - which I wear all the time, for that very reason.