I don't think that there is, honestly.
Compare flaming to a simple +1 enhancement bonus. If you're using a greatsword (and most people seem to be), a +1 enhancement bonus is simply better. You can use Power Attack to convert that +1 bonus to attack and damage rolls into a +3 bonus to damage rolls, which is only 0.5 points of damage less than a flaming weapon, except that the enhancement bonus is multiplied on critical hits, isn't affected by fire resistance, and doesn't require a standard action to activate. The best argument in favor of a flaming weapon is greater magic weapon. Without that, I don't think magical special abilities that give a bonus to damage rolls really have a reason to be, other than the alignment properties use in overcoming damage reduction.
Compare flaming to a simple +1 enhancement bonus. If you're using a greatsword (and most people seem to be), a +1 enhancement bonus is simply better. You can use Power Attack to convert that +1 bonus to attack and damage rolls into a +3 bonus to damage rolls, which is only 0.5 points of damage less than a flaming weapon, except that the enhancement bonus is multiplied on critical hits, isn't affected by fire resistance, and doesn't require a standard action to activate. The best argument in favor of a flaming weapon is greater magic weapon. Without that, I don't think magical special abilities that give a bonus to damage rolls really have a reason to be, other than the alignment properties use in overcoming damage reduction.