  We substantiate a covariant proposal for the holographic reflected entropy in
$CFT$s dual to non-static $AdS$ geometries from the bulk extremal entanglement
wedge cross section in the literature with explicit computations in the
$AdS_3/CFT_2$ scenario. In this context we obtain the reflected entropy for
zero and finite temperature time dependent bipartite mixed states in
$CFT_{1+1}$s with a conserved charge dual to bulk rotating extremal and
non-extremal BTZ black holes through a replica technique. Our results match
exactly with the corresponding extremal entanglement wedge cross section for
these bulk geometries in the literature. This constitutes a significant
consistency check for the proposal and its possible extension to the
corresponding higher dimensional $AdS/CFT$ scenario.
