@Chemus, nope. RAW text is you make the choice (singular) - apply this effect to X, Y, or Z - per attack (limiter). Not you make that choice three times for each ability or whatever you think you're reading. And since it says or instead of and each time you make the choice, again only once per attack instead of multiple times, you can only choose one ability instead of all three. Also you didn't address stacking either and overlooked it. Remember, RAW stands Rules as Written and not bastardized opinions are fact.
Benefit: When you gain extra damage from a sneak attack, sudden strike, or skirmish, you can choose for the extra damage to be fire damage. If you apply this effect, increase the extra damage dealt by 1d6 points. Make this choice for each attack after it is resolved but before damage is dealt. This is a supernatural ability.
First, the 'or' is the only possible sensible word; 'and' would require that the abilities be used simultaneously for the effect to function at all, and it was not used. As Amechra said, the word is ambiguous; it can be exclusionary (Are you A, B, or C? B? Oh, I'm sorry, this line is for A's only), or not (Are you A, B, or C? A? Well, as long as you're one of the three, you get the stuff.) Guess which fits here?
B, the gate is 'when you gain extra damage from a sneak attack, sudden strike, or skirmish,'
III.: the result of unlocking the gate is 'you can choose for the extra damage to be [energy] damage.'
Also, another gate: 'If you apply this effect,'
5- the result of unlocking this gate is: 'increase the damage dealt by 1d6.'
Then, instruction; when you can make the choice to add the effect: 'Make this choice for each attack after it is resolved but before damage is dealt.'
Senarily, there is an addendum: 'This is a supernatural ability.'
The effect is eligible to be applied
to the extra damage whenever it occurs, choice is made at the resolution of the attack, prior to damage resolution. Each extra damage is discrete, and each explicitly stacks with the other. The (Su) clause checks for AMF on attempting to apply the effect. These are the RAW.
Results: An invisible, silenced blue dragonwrought kobold Rog1/nja1/sct1 with str 8, and cha 11, having taken DFS as 3rd level feat, moves 10' and claws at a 3rd level dwarf fighter, hitting on its attack roll.
The attack resolves, it gets extra damage from sneak attack (no dex, due to invis.), sudden strike (also no dex), and skirmish (moved at least 10').
Extra Sneak Attack damage, '
y' or '
n'? Y, 1d6
Decision: apply DFS to extra damage from Sneak Attack, '
y' or '
n'? Y
Gate: Antimagic area, '
y' or '
n'? N
Result: extra damage is electricity, add 1d6 to it.
Extra Sudden Strike damage, '
y' or '
n'? Y, 1d6
Decision: apply DFS to extra damage from Sudden Strike, '
y' or '
n'? Y
Gate: Antimagic area, '
y' or '
n'? N
Result: extra damage is electricity, add 1d6 to it.
Extra Skirmish damage, '
y' or '
n'? Y, 1d6
Decision: apply DFS to extra damage from Skirmish, '
y' or '
n'? Y
Gate: Antimagic area, '
y' or '
n'? N
Result: extra damage is electricity, add 1d6 to it.
Damage resolves: 1d2-1 slashing, plus 1d6+1d6 Sneak attack electricity, 1d6+1d6 Sudden Strike electricity, 1d6+1d6 Skirmish electricity damage all added to attack.
Rolling damage: 1d2-1 (8 str) claw, +6d6 electricity damage [average result: 1 slashing damage +21 electricity]
Gate: Electricity resistance or immunity, '
y' or '
n'? __