No fancy ignition mechanism is needed. There are bacteria that produce phosphine (e.g. by reduction of phosphates), which spontaneously ignites in air. Combine them with those producing methane, and we have a self-igniting composition. (Actually, the diphosphine, P2H4, is the spontaneously igniting form. Some germs reportedly produce it together with the phosphine.)
Also, why methane? Why not a higher alkane? There are bacteria producing propane being discovered on the seafloor. Propane can be stored under reasonable pressure at dragon’s body temperature in liquid form, so no significant additional bulking up of the dragon is needed. The pressure release further disposes of the need of powerful lungs (though these can be assisted with the wing-beating chest muscles, as these have to have significant power anyway). The gas will escape under its own pressure, like a carrier gas from a spray can. The cooling from the evaporation may be however fairly unpleasant for the dragon (but may be also used to e.g. precool blood for heat removal from mouth or flame-facing surfaces; blood is a fairly good heat exchange medium and is easily routed through the body).
For protection of the dragon’s own mouth against the fire, saliva (possibly gelled into a slime to stay in a sufficiently thick layer) and Leydenfrost effect should do a good job for non-sustained, burst flame production, together with most of the fuel-air mixing occuring outside of the dragon. A laminar coaxial flow of air from the lungs can also assist, forming a protective layer between the dragon and the flame, not unlike it is being done in rocket or jet engines to protect the nozzle or turbine blades.
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