"They say that the owl named Kaepora Gaebora is the reincarnation of an ancient Sage."
So no, he's not a reincarnation of the Great Deku Tree. What sage he was we just don't know. Some people think Raru, but Rauru was the only ANCIENT sage that didn't have to be awakened, so he has been around longer than the other sages you awaken in
OoT. Some think it's possible that he took the form of Kaepora Gaebora to guide Link, but if I recall correctly, you see him once as Adult Link at the Spirit Temple... in that case, we've already met Rauru, so he'd have no reason to be in the form of an owl.
Therefore, I doubt he's Rauru. I figure he was a different sage of sorts... maybe of Wind. Who knows.