Where is there a rabbinic discussion of whether eternal Gehinnom (i.e. eternal judgment leading to eternal punishment) negates the concept of Reincarnation? (Because the concept of reincarnation, if true, sounds like one is able to escape such eternal consequence, if there is one.)
This answer is assuming the reincarnation of the OP is not rival of the dead, as clarified in the comments, but is referring to what is commonly called Gilgul Neshamos.
As I mention in my answer to this Mi Yodea question, the wise men of Luniel mention this idea to the Rashba, written in his responsa 418. Rashba did not argue against their logic, but he didn't vocally endorse it either. His having printed can be taken as having accepted it.
However, there are two points which I'll mention that negate the argument.
The first point is according to most Kabbalistic works that I've seen which discuss the subject of Gilgul, such as Chida and Ben Yehoyada. The entire soul is not transmigrated to a new body. Rather, a 'spark' (nitzutz) of the old soul which needs fixing is attached to a new soul. So the old soul who sinned is still punished in Gehinom, hell, while that spark that needs fixing is in a new host on earth.
The second point is not something I've seen in books but have heard some Rabbis say. Being sent back as a Gilgul is more painful to the soul than Gehinom. If that is true, the returning itself is in fact punishment and the soul was not spared any punishment by this process. (As noted I've never seen this inside and can't vouch for it's truthfulness.)