Maybe i shouldn't post since i don't really have a clue, but...
Make a new blink which costs 0 mana, then another skill - lets say "fireball" (since it has to be a target spell i think) - and lower that so it doesn't do anything.
Give the hero you want the doublestrike on the "fireball" ability and then when he clicks that he would be ordered to blink to his target, then attack, then blink again and attack.
could look like this.
Event: Unit starts the effect of an ability.
Condition: ability being used/manipulated equals to "fireball".
Action: Unit - order "your unit" to blink to the target.
Action: Unit - order "your unit" to attack the target.
repeat the actions as many times as you want.
I'm not sure this will work, just popped out of my head :roll: