If a character soaks their weapon in oil and ignites it, what kind of damage does it do?

Looking at the description of how oil & torches work my guess is that it does normal damage, +1 fire damage per round the weapon is aflame (2 rounds?). If the target is soaked in oil (say from a hurled flask) they take an additional 5 fire damage (for 2 rounds?)

Related to How much damage do torches used as improvised weapons do? but not a duplicate. That question specifically focuses on torches and whether they can be used as a blunt object in addition to doing fire damage. That question's answer is kind of a punt because torches ultimately aren't made to be used as clubs, and anyway it doesn't answer this question.