Flow value over edges in Max flow/Min Cut Ford Fulkerson
Yes. More precisely, for every min cut $(W,\bar{W})$, there is some max flow $f$ such that $f(x,y)=0$ if edge $(x,y)$ goes from $\bar{W}$ to $W$, and $f(x,y)$ equals the capacity of $(x,y)$ if edge $(x,y)$ goes from $W$ to $\bar{W}$. This is usually proven using the linear programming formulations of min cut and max flow, and follows by the complementary slackness property.