Interesting question.
It would explain why there have been people in history who not only were "ahead of their time", but also seemed to be able to get faint glimpses of things that happened later (aka predicted the future). What if they remembered future lives which for them were past lives?
But then, how can you have free will when you reincarnate into a scenario where everything already has happened? As an average person, you won't really change history, but still you would affect others on a minor scope, and how would this work when you can't change the past?
Or does past life amnesia or your life plan prevent you from doing anything you "shouldn't"?
Or is free will an illusion?
Can make one's head swirl, similar to time travel.
Yet I kinda like the idea that it's possible.