  In this paper, first, we give an explicit formula for the flag curvature of a
homogeneous Finsler space with generalized $m$-Kropina metric. Then, we show
that, under a mild condition, the two definitions of naturally reductive
homogeneous Finsler space are equivalent for afore said metric. Finally, we
study the flag curvature of naturally reductive homogeneous Finsler spaces with
generalized $m$-Kropina metric.
