Since a sonic boom is just a collection of pressure waves combined into one massive pressure wave, would the low pressure zone behind it be enough to put out a large fire?
Acoustic suppression of flame is viable. It can happen in one of two ways:
(1) Continuous sound waves may interact with flames and accelerate air and vaporized fuel particles, which drops the temperature of the flame and disrupts the flame boundary layer between the hot gas flame and the vaporized fuel. When flames are extinguished, vaporized fuel ceases to burn. However, if un-vaporized fuel remains hot enough, it will flare up again when the sound waves cease.
(2) A shock wave, or blast wave, may displace hot gas and vaporized fuel from the source of a fire, and spread it over a wide area, cooling it and extinguishing the flame. This method is used with oil and gas wellhead fires. If un-vaporized fuel at the wellhead remains below combustion temperature, this allows time for firefighters to stop the flow of fuel.
It's not so much the low pressure zone behind a shock wave, as it is the displacement effect of the wave front that extinguishes flame by accelerating and dispersing vaporized fuel (either from liquids or from burning solids) and hot gas, separating fuel vapor from the hot gas of the flame.
If the energy in a sonic boom emanating from an aircraft high in the atmosphere were great enough, it could disperse flames. But I doubt such energy could be achieved unless the wavefront were concentrated into a small area. Pressure at ground level caused by sonic booms generally is under two pounds per square foot.
Alternatively, a shock wave emanating from a powerful explosion (nuclear, dynamite, etc.) can extinguish flames. But if unvaporized fuel remains at combustion temperature, it will flare up again.