  The astrophysical origin of stellar-mass black hole (BH) mergers discovered
through gravitational waves (GWs) is widely debated. Mergers in the disks of
active galactic nuclei (AGN) represent promising environments for at least a
fraction of these events, with possible observational clues in the GW data. An
additional clue to unveil AGN merger environments is provided by possible
electromagnetic emission from post-merger accreting BHs. Associated with BH
mergers in AGN disks, emission from shocks emerging around jets launched by
accreting merger remnants is expected. In this paper we compute the properties
of the emission produced during breakout and the subsequent adiabatic expansion
phase of the shocks, and we then apply this model to optical flares suggested
to be possibly associated with GW events. We find that the majority of the
reported flares can be explained by the breakout and the shock cooling
emission. If these events are real, then the merging locations of binaries are
constrained depending on the emission processes. If the optical flares are
produced by shock cooling emission, they would display moderate color
evolution, possibly color variations among different events, a positive
correlation between the delay time and the duration of flares, and accompanying
breakout emission in X-ray bands before the optical flares. If the breakout
emission dominates the observed lightcurve, it is expected that the color is
distributed in a narrow range in the optical band, and the delay time from GW
to electromagnetic emission is longer than $\sim 2$ days. Hence, further
explorations of the distributions of delay times, color evolution of the
flares, and associated X-ray emission will be useful to test the proposed
emission model for the observed flares.
