Sublattice distortion resulting from alloying compositionally distinct double perovskites is shown to influence photoluminescence emission in Cs2Ag1-xNaxBiCl6 (0 < x < 1). The end members show negligible photoluminescence, whereas interestingly the alloys exhibit broad photoluminescence. These emissions are attributed to self-trapped excitons (STE) resulting from sublattice distortions arising due to the mismatch in [AgCl6]5- and [BiCl6]3- octahedra. Change in sublattice distortions plays significant role in the formation and recombination of STEs. The STE emission intensity and quantum yield greatly depend on x, with highest intensity observed for x = 0.75, consistent with a large change in sublattice found at this x. Variation in photoluminescence properties with composition follows a similar trend as that of bandgap and phonon vibrational changes observed due to sublattice distortion. Temperature-dependent phonon vibrations and photoluminescence studies reveal a giant electron-phonon coupling. A strong synergy between STE emissions, electron-phonon coupling, bandgap, and phonon vibrations in double perovskites with sublattice distortions is demonstrated.