Helmets are in extremely short supply in both the kingdom and empire's camps, it seems. A crafty merchant could still make a fortune by stockpiling them and then selling them before an especially crucial battle.
Although rain can't just put out oil-based flames, I doubt it'll combust that quickly even with hay in that weather.
They'd have to wait for it to spread and gradually produce smoke.. Know what'll be more effective? A Hwacha... with firework tips, it'll scare the shit out of those horses.