A biblical "kind" may refer to a phylum.
I am not sure how you could make a claim like this with a straight face... I assume you may not have meant "phylum" but your post continues with the claim, so maybe you are not clear on what a phylum is...
Anyway... as Dwise1 explains, the concept of "kinds" was invented because it became obvious that 2 individuals of every modern species would not fit on the ark, so the thought was there must have been a reduced number of species that later diversified. But there is no real reason to believe this. The Bible doesn't make the claim that organisms diversified after the flood. There is no objective definition of "kind" - it is merely "intuitive". The whole concept of "kind" is arbitrary and speculative.
A worse problem is that according to the Biblical record, a "kind" can only give birth to its own "kind". So lets assume that a kind is roughly equivalent to family (as many creationists propose - I think you are the only one I have heard propose phylum). We will use
Felidae (the cat kind) as an example. Lets say the creature that left the ark was the species
Felidae beta. But according to the Bible,
Felidae beta could only give birth to
Felidae beta babies, but there are now over 40 extant species of
Felidae plus numerous extinct species. How did that occur? At what point did
Felidae beta give birth to a
Panthera tigris or a
Lynx rufus or a
Felis catus. What is the mechanism of change between these types of cats? At some point,
Felidae beta must have given birth to all these other species.
Even if they are all the same "kind," it seems as if this violates your premise that kinds don't give birth to different kinds. Do you expect a panther to give birth to a puma, or to a lion, or a cat?
So, what is the mechanism of change within a "kind"?
HBD
Whoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca"Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem.
Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.