Fire is a very dangerous element to work with. There are many products fire specialist use that helps in the safety of using fire in stunts.
A stunt coordinator supervises the safety during a scene when there is fire present. A SFX Supervisor is usually responsible in generating the fire on the set. This is done from the fuel that is use and what they have on fire. Many times it is called for a controlled fire a the the SFX crew will set up flame bars that has propane running through it and can be controlled to get bigger or smaller at the control a gage.
Fire specialist have a lot of experience working with different fire retardants, fire gels and fuel ignitors. Some use these skills for live shows, commercials or feature films.