All fires are oxidation reactions, but there is no single chemical equation that describes all fires. The exact chemical equation for fire varies based on the fuel, the oxidizer used and the atmospheric conditions surrounding the fire.
Fires produce heat because oxidation is an exothermic reaction. All fires consume oxygen and release heat as part of the reaction, but other products of the reaction depend on the fuel. Organic materials produce water and either carbon dioxide or carbon monoxide as they burn. What gas is produced by the reaction depends on how much oxygen is available. Oxygen-poor reactions produce carbon monoxide, and oxygen-rich reactions produce carbon dioxide.