Oxygen itself isn't flammable, but reacts with other chemicals in a reaction so exothermic that it causes combustion of the material with which is reacts.
As for your question about water - H2 and O2 alone are indeed fire risks. However, you need to remember that the properties of a molecule comprised of various elements often differ greatly from the proterties of these constituent elements. For example, carbon isn't toxic (it is used as a stomach was after overdose) and nitrogen is the main gas in the atmosphere, but if you combine them to form the CN- ion, you have cyanide, which certainly won't do you much good. Also, while iron is magnetic, several iron compunds are not.
Good question though.