Yes I need to test it. Its not clear. Its just that I needed to know quickly as I was in the middle of an MP game and it was (very) relevant. Game Over (I lost) and I never got the chance to try it but now I need to satisfy my curiousity. I will post my results.
I may be wrong but my best guess is that a flambeau does normal damage (x3 vs undead) with an added chance to set the enemy on fire. You'd be immune to the extra fire, but the sword would still hurt a fire immune creature.