It's a low magic campaign but Trolls a fairly high magic creatures, though not overtly so. So why not adjust the trolls? Trolls have fast healing as long as they are not burning and take double damage from fire. That way the troll has a similar flavor but any flaming weapon mechanic you choose should be fairly effective.
As far the mechanic itself, I thought there was a rule somewhere about torches dealing damage as clubs +1d4 with a chance of being extinguished with each hit.
I would suggest the flaming weapon deal normal damage -1 +1d4 fire with a chance to catch a hit target on fire. The pitch, once ignited lasts 3+1d6 rounds but each swing has a 20% chance of extinguishing the flame. (if relit, do not reroll duration) If you want to roll excessive amounts of dice, each hit has 50% chance of pulling off some of the pitch reducing the remaining duration by 1 rnd.