The oxygen is used to get the flame hotter. Oxygen is what allows things to burn. With no oxygen, there is no flame. Oxygen in the air will allow a propane or natural gas fuel to burn, but not at its maximum temperature. This is where oxygen comes in.
Oxygen is not flammable, but oxygen will cause any flame to be MUCH bigger than it would be. So oxygen does fall into the category of a burning hazard.
To learn how oxygen effect a flame you can see our terms and techniques