My party is about to encounter some trolls. I've been giving them hints that this was coming up and they have gotten some flaming weapons. I'm trying to figure out if one of them has a flaming burst broadsword, will it set the troll ablaze with out a critical hit if the PC is using it as a standard flaming weapon.
A flaming or flaming burst weapon can deal 1d6 fire damage on a hit, if that feature has been activated. Fire damage by-passes a troll’s Regeneration, dealing lethal damage and eliminating the healing for a turn. Setting it on fire is not necessary to damage a troll.
On the other hand, fire damage does not automatically start a fire; for the most part, fire damage burns a creature but doesn’t ignite it. Unless something explicitly says that it sets a creature on fire, assume it does not. This applies equally to fireball as it does to flaming weapons. Most organic creatures do not ignite easily, after all. This includes trolls.
You didn’t ask, but worth mentioning: scoring a critical hit with a flaming burst weapon changes nothing here except for the total damage dealt.
Most normal creatures contain a lot of water, very old zombies, and mummies don't, trolls would usually. Unless doused in oil they shouldn't start on fire. If your adventures aren't so equiped if they are not the first to attempt to take on the trolls they may find oil in the back packs of eaten bodies.