Excellent article by Cecil, but oxygen is not necessary for fires or flames. Hydrogen and Fluorine is an example. Aluminum and Fluorine can also be an example.
Flame is the combustion zone of a fire, flame is the region where heated incompletely burned particles give off light before they cool down.
Most gas flames are invisible because there are no particles to give rise to the flame. And that does’nt include CO or Hydrocarbon fires because CO and hydrocarbons disassociate to give C (soot) particles which again end up giving a visible flame.
Now, about hydrogen and fluorine: it seems to me that it’s not unreasonable to define “fire” as necessarily requiring oxygen, since people normally encounter fire in an oxygen atmosphere, and why not have a shorthand term for rapidly combining with oxygen? Then, I suppose, fluorine + hydrogen exhibits a “fire-like behavior.” That’s not to say that I necessarily disagree with you; if it walks like a duck and talks like a duck… Just sayin’ I’m ambivalent, is all.