What is the chemical formula of fire?

Fire is basically an oxidation process, which starts when a flammable and/or a combustible material with an adequate supply of oxygen or another oxidizer is subjected to enough heat and is able to sustain a chain reaction.

This starts a fire.

Combustion or burning is a complex sequence of exothermic chemical reactions between a fuel and an oxidant accompanied by the production of heat or both heat and light in the form of either a glow or flames.

Direct combustion by atmospheric oxygen is a reaction mediated by radical intermediates. The conditions for radical production are naturally produced by thermal runaway, where the heat generated by combustion is necessary to maintain the high temperature necessary for radical production.

In a complete combustion reaction, a compound reacts with an oxidizing element, such as oxygen or fluorine, and the products are compounds of each element in the fuel with the oxidizing element. For example:

CH4 + 2O2 → CO2 + 2H2O

CH2S + 6F2 → CF4 + 2HF + SF6

A simpler example can be seen in the combustion of hydrogen and oxygen, which is a commonly used reaction in rocket engines:

2H2 + O2 → 2H2O + heat

The result is simply water vapor.

In the large majority of the real world uses of combustion, the oxygen (O2) oxidant is obtained from the ambient air and the resultant flue gas from the combustion will contain nitrogen:

CH4 + 2O2 + 7.52N2 → CO2 + 2H2O + 7.52N2 + heat

As can be seen, when air is the source of the oxygen, nitrogen is by far the largest part of the resultant flue gas.

In reality, combustion processes are never perfect or complete. In flue gases from combustion of carbon (as in coal combustion) or carbon compounds (as in combustion of hydrocarbons, wood etc.) both unburned carbon (as soot) and carbon compounds (CO and others) will be present. Also, when air is the oxidant, some nitrogen will be oxidized to various nitrogen oxides (NOx).