I agree any request for immediate eligibility for a transfer is a long-shot. But there are a couple extenuating circumstances here that might make it more plausible. First, he was (apparently) involuntarily dismissed from his former program. Second, he's already missed one season due to injury. So if a waiver isn't granted, he'll effectively lose a season of eligibility through no fault of his own (setting aside whatever it was that he did to lead to his dismissal in East Lansing).
Even if this waiver is denied, I think there would be a chance he could seek a 6th year of eligibility down the road.
Dismissal from the team does not mean dismissal from the school unfortunately. So he would still have to transfer school credits from MSU to Ohio. Technically speaking, that should matter to the NCAA but we've learned in the past that even though schools are associated with the NCAA and athletic teams are also, the two are not always mutually exclusive.
I would say it probably depends on what Kaminski did in order to be dismissed. Dorial Green-Beckham just tried the same thing after being "dismissed" from Missouri and his transfer to Oklahoma. It was recently denied and I have no doubt his run-ins with the law had something to do with it. Hopefully that is not the case with Kaminski.