Less painfully, sure just wear long sleeves. 100% cotton to be on the safe side. If you're wrapping on bare skin, you can expect a few "minor singes" from time to time, mostly from contact with hot metal.
The worst thing that CAN happen if your not careful is having a chain wrap and knot around a limb, I'm sure you've experienced this during your practice sessions. Don't panic if it happens, simply spin your body around in circles that use centrifugal force to "pull" the flames away from the entangled limb until your safety arrives with a wet towel.
And, watch for fuel transfer to your clothing if you decide to wrap too early into your burn.