As for sources in the Gemara, as I said, you won’t get open ones because it was a Sod. However, there are certain references that can be taken to be alluding to, or based on, Gilgul. We have the Gemara in Bava Kamma that describes what happens to one who doesn’t bow by Modim. After seven years he turns to one animal, then another and another. Unless you want to totally conceptualize this Gemara and make Adobe lesson out of it, it is hard to think it means that his body will transform. Therefore, many learn that it is referring to him becoming Megulgal.
Then we have these statements of this one being that one, for example, Bilaam being Lavan. In this case, the ibn Ezra points out how hard it is to accept that Lavan lived that long. Therefore, the ibn Ezra says it is a Sod. The Maharal likewise explains, in his own terminology, that this is what Chazal mean when they say Memuchan is Haman. This is also the only way to reconcile the many conflicting statements about Eliyahu Hanavi. Is he a Kohen? Pinchas? From Gad, as he testified in Tanna Dibei Eliyahu? From the children of Rachel?