How can I extinguish myself?

Once you've been set aflame, there is only one way to extinguish yourself: stepping onto a water square (including fountains). This is guaranteed and has immediate effect; oddly, you don't need to step into the water, levitating above it is fine.

Conservation is checked on each potential item destruction, so if you wear an amulet of conservation while aflame, you reduce the chance of every surviving item being destroyed by 90% each turn.

(Source: reading the DCSS 0.8 source code.)