Maybe an indirect way of finding an answer is to find out how many kinds were on the ark? I don't know the answer to that question, but perhaps someone else does. If there were, say 50 kinds of animal, then one needs to split out all the animals alive today into 50 categories... but this is certainly far from an explanation of what "kind" means in clear terms. I don't think there can be an answer to that, though, as having a clear definition would mean the beginning of the end for Ken Hamm & co.
Just think how much change must have happened with a bottleneck event like the great flood wiping out everything except what was on the ark. Then, in the last few thousand years, animal diversity could somehow reach the level it is at today, but there is still some sort of mechanism to prevent things from changing between "kind" - like an asymptotic approach to a new kind but the threshold can never be crossed. How could things change so much, and so fast, but it's somehow illogical in the YEC mindset that the "kind" line can never be crossed?