Garey and Johnson, page 214, $K$th Shortest Path:
Given a graph $G=(V,E)$, a positive integer length for each edge, specified vertices $s,t$, and positive integers $B,K$, the question whether there are $K$ or more distinct simple paths from $s$ to $t$ each of length $B$ or less, is not even known to be in NP.
This doesn't quite answer your question, since it does not require the paths to be vertex-disjoint, but it may show you where to start looking.
See also page 217, Maximum Length-Bounded Disjoint Paths: given a graph, two specified vertices, and two positive integers $J,K$, does the graph have $J$ or more mutually vertex-disjoint paths joining the vertices, none involving more than $K$ edges. This one is NP-complete, and actually looks more relevant than the first one.
Best Answer
Split each undirected edge $\{v,u\}$ of the graph $G$ into a couple of two oppositely directed directed edges $(v,u)$ and $(u,v)$ of capacity $1$ (or by a cycle $v-[vu]-u-[uv]-v$ with two added dumb vertices $[vu]$ and $[uv]$, if you have doubts dealing with directed graphs with coples of two oppositely directed directed edges). It is easy to check that both the initial graph $G$ and the splitted graph $G’$ has the same values for a maximum $s$-$t$ flow, maximum number of pairwise edge-disjoint paths from $s$ to $t$, and a smallest $s$-$t$ cut. You can read more about proofs of the equalities of all these values and algorithms for their calculation in Lectures 2-4 from our block course "Algorithmic Graph Theory”.