If your oxygen concentrator is working correctly it will pull oxygen from the air AND STORE IT. The only time oxygen will be dispensed from the concentrator is when the PATIENT inhales. Oxygen should not flow except when the patient inhales. The patient breathes in the Oxygen and exhales a normal breathe. The concentration of oxygen from the patients exhaled breathe will be no greater than a person breathing unassisted.
Oxygen is nonflammable it is however an accelerant in that an oxygen enriched environment will support combustion better than a normal atmosphere. This enriched oxygen environment is what made the fire so bad on the space capsule.
I doubt if your pilot lights in the rig will cause any harm as there should be no build up of oxygen in the rig IF THE CONCENTRATOR IS FUNCTIONING NORMALLY. There is NO CONTINUOUS release of oxygen from a concentrator.