The best solution is inherent FR polyester, because it starts us off with a naturally high base level of fire resistance. This guarantees that fire retardant fabrics look and feel just like natural ones, and that's even before they undergo rigorous testing for high safety standards!
Certain textiles do naturally resist fire better than others. For example:
Wool is generally considered the most fire retardant natural fiber, as it is difficult to ignite and may extinguish smaller flames on its own.
Silk also burns slowly, is difficult to ignite and may self-extinguish under certain circumstances.
Acrylic, polyester and nylon are also all considered fire retardant fabrics, as they catch fire at a much higher temperature than natural fibers.