Smuggler or Spy.

Use when a hostile figure enters an adjacent space. Gain movement points equal to your speed.

I really like this for running away form Royal guards and Darth Vader.

If you had two of these cards in hand (it is a card you can take two of) could you play both of those at once?

Imagine Vader strolling up to Jynn and then she drops two of those cards and runs away 10 spaces. That's crazy!

Is this allowed?

I'll could be wrong with this but Im gonna say you can't use it on the same figure twice. The first time Vader triggered the card by entering an adjacent space. So now Jyn interrupts his action to move 5 spaces. Vader is no longer entering an adjacent space to Jyn so a second copy could not be used on her. However I do believe you could use the second copy on a different figure. Vader enters a space that Han and Chewie are adjacent too. You could then play Slippery Target on Han and get him out of the way and then Slippery Target on Chewie.

Thats how Id rule it.

I would assume you can't either, but it says you gain movement points, not that you have to move. So couldn't you play both of them to gain the points, kind of bank them up, before you move?

If you gain movement points outside your activation you must spend them or lose them.

As has been said, when receiving movment points outside your activation they must be used immediately or they are lost. In addition there is this under Command Cards in the RRG:

"A player cannot play multiple copies of the same Command card at the same time. For example, if a card provides “+2 Accuracy,” the player cannot play two copies of the card to gain +4 Accuracy for one attack."

Thanks for finding that. I had been too lazy to really look through the rules but couldn't remember reading anything like that. Guess its time to re-read through all the rules just to make sure I haven't missed any other little things like this.