Good points have been made in the thread. Something I keep in my truck for work is a set of nomex flight gear (flight suit, gloves, beanie), leather boots and a mix of nomex and wool underwear. Would it be worth the delay getting to the victim to put the nomex clothing on before I approached?

It would slow me down getting to the victim, but the time dressing up would be used evaluating the scene from a distance and planning a course of action. If a fire did happen, I'd be able to egress without bringing too much fire with me. The gear I mention won't allow me to stay in the fire, it will only allow me a few more seconds to escape without serious burns. Nomex won't melt or support flame, but it does char and then disintegrate.