Oxygen does not burn on it's own and is not flammable nor is oxygen explosive.
However oxygen can fuel a fire that is already near it so if you catch your clothing on fire or get a lit cigarette near the oxygen then the oxygen can cause the cigarette to catch your clothing and body on fire.
So you should never smoke when on oxygen because the oxygen can fuel a fire.
A fire needs oxygen to burn so that oxygen will accelerate and help the fire burn faster but the oxygen itself is not flammable.
Oxygen is in the air around us as well and we all breathe in oxygen and it's not flammable or explosive but a fire can spread fast when oxygen is introduced to the fire.
So the oxygen in the tank if leaked out where the fire is can spread the fire or if you get a cigarette near the oxygen you're breathing in then a fire can result from that as well.