Okay this is a girl who not only still likes her ex, but kissed you and flirted with you, and at the same time was supposedly going out with someone else. Don't you think that is just a little odd?
She sounds like she can't stay with just one person :/ or is just really damn confused. If she likes you more she shouldn't even be going on that date and putting you and her through the awkwardness.
I think you should move on, considering she's going away for a long time, she might even find someone wherever she is going, and you won't risk things going bad between you and your friend, especially if it was a bad relationship, because not dating a friend's ex is meant to be one of the top friend rules dude
And I think you should wait till she comes back, then maybe she'll have some time to think about who/what she really wants.