How do we understand the biblical "kinds"? A fair, but difficult question. To understand the difficulty, we must first compare the concept of "kind" to its evolutionary equivalent.
Evolution believes that all of life evolved from a single living cell, moving through many stages of increased morphological complexity en route to the diversity we now witness.
Obviously, this means that life passed through a number of evolutionary watersheds, and these major transition points are afforded categories under the science of taxonomy: kingdom, phylum, class, genus, order, family and species.
For the most part, this has been an orderly process; there has been some reclassification and reallocation, but that's to be expected.
"kinds", on the other hand, suggest that biological diversity had a much more complex starting point; from a set number of highly complex organisms aboard the Ark, through speciation, to the multiplicity of species we encounter today.
I agree with many other people that "family" is the taxonomic level that best approximates "kind". But as taxonomy has seen some retrospective reshuffling (and no doubt will see more in the future) "kinds" will not neatly fit into the "family" classification, and will also need ongoing revision.
For me the solution is simple. I would place creatures of obvious phenotypic similarity into the same Kind- as long as they did not exhibit a genetic complexity greater than that exhibited by the majority of established members of that Kind (increased genetic complexity being defined as more coding DNA, resulting in a biological feature or function additional to all of those enjoyed by the other members.)
This would allow for the diversity created by simple speciation, without requiring the problematic increase in genetic complexity which, as we all know, has never been observed or documented.
Polymer-metabolising microbes not withstanding, of course.
"When man loses God, he does not believe in nothing. He believes in anything" G.K. Chesterton