The way Burst weapons work is as such:
as flaming, but "Burst weapons deal 1d10 point of bonus damage on a successful critical hit." for every X past 2, an extra 1d10 is dealt, I.E. x3 = +2d10, X4 = +3d10.
So, the 1d6 for the flaming, sonic, whatever is always dealt, and if there is a crit, you add the d10's as well. So if you were to crit with a scythe, for example, you would deal base weapon damage + 1d6 + 3d10.
Tada.
As for the argument that fire and cold enchantments etc. do not mix, I disagree. You could work it out several ways to describe why they would not negate each other.
1 - The fields of flame and ice surrounding the weapon could intertwine, but not actually come into contact with one another. Therefore the ice does not contact the flame, and vice versa. Instead, they simply repel each other, causing no ill effects.
2 - While on the weapon, the cold and fire enchantments swirl around the weapon, visually appearing to be battling one another, yet their elemental forces do not come into play until the weapon hits what it is swung at, at which point the fire and cold are emitted in a single instant, both chilling and burining the victim.
3 - They just work. They're magical, so you could say that "Magic finds a way."
Come to think of it, dealing fire and ice damage in the same blow should actually do more than just the individual damage for fire and ice. They're in antipode, you know? Ever add ice water and boiling water into a glass pitcher at the same time? The damn thing shatters. The effect should be similar for the damage of the weapon.