Before walking on burning coal people wet their feet. When people start walking on their feet releases some sweat. Their sweat or moisture evaporates when people start walking on coal and forms a protective layer beneath their feet.
So, a person walking on coal does not actually walk on coal. They are walking on a protective layer of water which does not burn their feet. This is because of low heat capacity and a poor thermal condition. Thus, in order to protect from burning one should walk fastly to avoid damage.
Another important role is played by coal which also protects the feet from burning. Coal and wood is a bad conductor of heat to pass quickly unlike metals which passes heat quickly.
On a contrast, if a person walks on a metallic plate there will be higher transfer of heat as metal is a good conductor of heat and therefore, the person’s feet will burn quickly.