  We theoretically investigate the superfluid density and
Berezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashba
spin-orbit coupled atomic Fermi gas with both in-plane and out-of-plane Zeeman
fields. It was recently predicted that, by tuning the two Zeeman fields, the
system may exhibit different exotic Fulde-Ferrell (FF) superfluid phases,
including the gapped FF, gapless FF, gapless topological FF and gapped
topological FF states. Due to the FF paring, we show that the superfluid
density (tensor) of the system becomes anisotropic. When an in-plane Zeeman
field is applied along the \textit{x}-direction, the tensor component along the
\textit{y}-direction $n_{s,yy}$ is generally larger than $n_{s,xx}$ in most
parameter space. At zero temperature, there is always a discontinuity jump in
$n_{s,xx}$ as the system evolves from a gapped FF into a gapless FF state. With
increasing temperature, such a jump is gradually washed out. The critical BKT
temperature has been calculated as functions of the spin-orbit coupling
strength, interatomic interaction strength, in-plane and out-of-plane Zeeman
fields. We predict that the novel FF superfluid phases have a significant
critical BKT temperature, typically at the order of $0.1T_{F}$, where $T_{F}$
is the Fermi degenerate temperature. Therefore, their observation is within the
reach of current experimental techniques in cold-atom laboratories.
