What kind of chemical reaction is fire?
You need oxygen for fire, and so a redox reaction is taking place. Oxidation only kind of is about oxygen. What it really is is the partial or complete loss of one or more electrons from an atom to a more electronegative atom (an atom that "wants" electrons more). Chlorine and many more atoms can also oxidize.
Anyways, it's oxidation because oxygen is attached to the stuff that's burning, and it's likely that oxygen is the most electronegative atom involved in the reaction, because heat is produced (oxidation reactions produce energy)