Well. As a chemist I associate a flame to the result of the reaction of any fuel with oxygen
But, it is not really in the chemical realm to be fair. It is technically a plasma. You know about the three states of matter right? Solid, liquid gas. Well if you heat a gas to very high temperatures (a flame fuelled by burning methane in oxygen can be 1500 degrees C) you ‘ionise’ the atoms and molecules that are in the gas. you get a ‘fourth state of matter’ – a plasma. My brother is actually a ‘plasma physicist’. Anything ou want to know about this just ask and I will get him in here. In a plasma, the electron(s) that were buzzing around the positively charged centre of atoms (the nucleus) in the gas state have come away from their orbits and we now have a ‘soup’ of positively charged ions and electrons.
You may have seen that different elements give different colours when they are placed in a flame: Sodium gives a very familiar orange colour (like in street lamps, because these are sodium vapour lamps). Strontium gives an awesome purple/lilac colour. Flames are usually orange because they usually come from burning some form of carbon and usually there is not enough oxygen around for complete reaction of the carbon in the fuel to CO2 and water. We know if we add oxygen (or open the valve up on the bunsen burner) we get a blue flame, and no soot. This is complete combustion and the flame temperature is much higher and different types of molecules are formed compared to those in low temperature flames. Those happen to give that blue colour. As for why there is any colour at all, well thats a another question …..ask me it!