This may seem like a silly question, but is there a flammable liquid that could oxidise itself, so it could effectively burn in a vacuum?
Indeed yes, and it's been used in all kinds of airless situations, including torpedos and rockets and I think even submarines. It's hydrogen peroxide, which when exposed to a catalyst will oxidize and reduce itself:
2 H2O2(l) -> 2 H2O(g) + O2(g)
You'll notice that the oxygens on the left are in oxidation state -1. Half of them become reduced to the O in water (oxidation state -2) and half become oxidized to the O in O2 (oxidation state 0).