Welcome to the boards Dareshiranu! I wouldn't worry too much about thread necromancy around here. It seems to be how we roll.
I keep it simple and in the tradition of the original game: 1d6.
Oil is difficult to get off and takes a while to burn. And by golly, fire is painful. So, an additional d6 on the next round, then one point thereafter for d6 rounds. Additionally, you can do nothing else but fight the flames for the duration.
As for the downsides... if the player is hit with an ignition source (fireball, fire trap, etc.), there's a chance that any oil carried will ignite, and incur the same d6+d6+1 damage routine on the player. Getting flaming oil ready requires a round with no movement or other action.
And besides, who says kobolds can't use flaming oil as well?