It depends. It should burn as long as the oxidizer and fuel are in contact and enough heat is provided to ignite it. The primary challenge might be the heat you’ll need for ignition. For effects of temperature and pressure, you’ll need to consider the phase changes of the oxidizer and fuel compounds used, how it affects their thermal properties as well. For depths like Mariana Trench (108 Mpa and 1 °C), I think an underwater flare would probably work if you provide enough heat to ignite it in the first place.
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