After doing some research, I found that any website that wrote about this said the same thing:
It works best with creatures that more closely resemble animals. Litten, Growlithe, Meowth and other bi- and quadripedal Pokemon will be fine with sharing a high-five.
That's the most I could find. This mostly likely does not encompass every Pokemon which can high-five, seeing as Mimikyu breaks this rule, (it doesn't resemble an animal, nor does it have limbs) but it is a good general guideline. I would test it but I don't have a DS. Maybe Sep can do another crazy test like he did with the Pokepuffs.