There is a little problem here though. You are ignoring other forms of oxidation and focusing singlemindedly on the one involving oxygen. What is the definition of oxidation?
ox·i·da·tion noun \ˌäk-sÉ™-ˈdÄ-shÉ™n\
1: the act or process of oxidizing
2: the state or result of being oxidized
Okay then, so what is oxidize?
ox·i·dize verb \ˈäk-sə-ˌdīz\
1: to combine with oxygen
2: to dehydrogenate especially by the action of oxygen
3: to change (a compound) by increasing the proportion of the electronegative part or change (an element or ion) from a lower to a higher positive valence : remove one or more electrons from (an atom, ion, or molecule)
See 3 there? Now, I mentioned Chlorine Trifluoride in another post. The chemical formula for that is ClF3. Where is the oxygen? This is an oxidizing agent, or oxidizer. It is a highly corrosive and otherwise nasty substance. Using this you can make sand combust, among other things. No conventional means of fire suppresson works on this substance, and that includes removal of all sources of oxygen. I dont know if any means of fire suppression works on it but the usual way to deal with a spill is to simply cool down all nearby fuel sources and wait for the reaction to end by itself.
Now, let us look at flammable as well to make sure it applies here.
flam·ma·ble adjective \ˈfla-mə-bəl\
: capable of being set on fire and of burning quickly
Let us also look at combust, since that is the term I have used about ClF3.
com·bust verb \kəm-ˈbəst\
: burn
And for you I will also include the definition made for kids.
: to be or set on fire : BURN
So, for something to be flammable it has to be capable of being set on fire. Combust means to set on fire. Seems we are on the right track. No oxygen involved and the substance is capable of causing combustion. Whats your next argument?