  We investigate the time evolution of reflected entropy and entanglement
negativity for mixed state configurations involving two adjacent and disjoint
intervals in the radiation flux of moving mirrors by utilizing the $AdS/BCFT$
duality. These measures are computed for the required mixed state
configurations by using the respective replica techniques in the large central
charge limit of the $BCFT_{1+1}$. We demonstrate that the results obtained
exactly agree with the corresponding holographic computations in the dual bulk
$AdS_3$ geometry with an end of the world brane. In this context, the analogues
of the Page curves for these measures are obtained for the required
configurations in the radiation flux of kink and escaping mirrors which mimic
the Hawking radiation from evaporating and eternal black holes respectively.
