  Active galactic nuclei (AGNs) have been proposed as plausible sites for
hosting a sizable fraction of the binary black hole (BBH) mergers measured
through gravitational waves (GWs) by the LIGO-Virgo-Kagra (LVK) experiment.
These GWs could be accompanied by radiation feedback due to the interaction of
the BBH merger remnant with the AGN disc. We present a new predicted radiation
signature driven by the passage of a kicked BBH remnant throughout a thin AGN
disc. We analyse the situation of a merger occurring outside the thin disc,
where the merger is of second or higher generation in a merging hierarchical
sequence. The coalescence produces a kicked BH remnant that eventually plunges
into the disc, accretes material, and inflates jet cocoons. We consider the
case of a jet cocoon propagating quasi-parallel to the disc plane and study the
outflow that results when the cocoon emerges from the disc. We calculate the
transient emission of the emerging cocoon using a photon diffusion model
typically employed to describe the light curves of supernovae. Depending on the
parameter configuration, the flare produced by the emerging cocoon could be
comparable to or exceed the AGN background emission at optical, and extreme
ultraviolet wavelengths. For instance, in AGNs with central engines of $\sim
5\times10^{6}$ M$_\odot$, flares driven by BH remnants with masses of $\sim$
100 M$_\odot$ can appear in about $\sim$[10-100] days after the GW, lasting for
few days.
