Maybe you could improve your chances of putting the fire out via rapid movement too? Equip burning items in hand and hit things with it?
Even better than hitting things, implementing a way to force an attack in a chosen direction. That could be used to help with fires on held items + your arms, along with kicking for legs. Then again, flailing around while you're on fire isn't exactly the most efficient method of putting yourself out IRL. Additional oxygen available etc. Would work for smaller fires though.
On dipping burning things into liquids, shouldn't vodka explode if you try to extinguish things with it?