I was thinking that it'd be an interesting idea if the Dragonborn was the reincarnation of an older form. Dragon souls are immortal in that they've always existed as far as we can tell, so unless the Dragonborn's soul was created at a later time, his soul shouldn't be an exception. One might assume that dragons can't be reincarnated like mortals can - only resurrected - based on the Shout used by Alduin to resurrect his followers, but I don't think we should rule out the possibility based on one example.
Alduin was able to restore the flesh of skeletons, so then, would his Shout have worked if the skeleton was incomplete? Surely it's not a stretch to restore a skeleton from a skull the same way one would restore flesh from a skeleton. His followers had their bodies kept intact in preparation for their resurrection anyway, so we may never know if Alduin's Shout was limited in that regard.
If we didn't know any better, we might assume that only dragons could have dragon souls, or rather, that dragon souls could only exist in dragon bodies. If dragon souls can exist in a non-dragon body, and if they can exist without a body for long periods of time, then there's not much of a difference between resurrection and reincarnation.
This is again assuming that the Dragonborn's soul has always existed. I think it's more interesting to say that his soul has lived many lives throughout history than to say that it's just been asleep all that time. Morrowind's story was interesting because you had a bit of an identity crisis after finding out that you were the Nerevarine. Maybe you felt responsible for your past actions and were motivated to finish what your past self began. Or maybe you didn't believe any of it because you didn't like being bound by fate. And it was a bit similar in Skyrim after learning the prophecy on Alduin's Wall. Maybe the Dragonborn of Skyrim was also a famous dragonborn in the past. Or maybe even a dragon.
So please share your thoughts, and any lore that either supports or refutes this idea.