I think you are wrong that he can time travel.

I think he has already lived EVERYTHING on the island from the moment the failsafe key was turned.

Think about it this way.

Des turned the key. His "life" flashes before his eyes right? Well also what flashes was an alternate reality where he didn't turn the key. So when he goes about on his days he see's differences in this alternate reality and present reality (ie Desmond saw that in the alternate reality lightning struck Claires tent killing Charlie so he changed it.) That is how he can "future see" and that is why the "flashes never stop."

Tell me what you think.