Subtyping and subkinding, are they relevant?
There will be no inconsistency. Those arise from shady postulates which state that some subkind is an element of itself, or that "too large" a kind/type is an element of a "too small" one (the most famous example is $\mathrm{Type} : \mathrm{Type}$), but that is not what we are dealing with here.

To give an example of what you're looking for, take $\mathrm{Type}$ to be the class of all sets. For the subtype and subkind relations we simply use subset and subclass inclusion. Take $a$ to be the class of all finite sets, and $b$ the class of all countable sets. Let $A = \{23, 42\}$ and $B = \mathbb{N}$. Then we have $A : a$, $B : b$, $A \subseteq B$, $a \subseteq b$, and both $a$ and $b$ are subkinds of $\mathrm{Type}$. And it would not be difficult to arrange $A \subseteq B$ and $b \subseteq a$, if we so wished.

Or you could take $\mathrm{Type} = a = b$ and $A = B$, but that's not a very informative answer, even though it has its virtues.