  We present numerical waveforms of gravitational-wave echoes from spinning
exotic compact objects (ECOs) that result from binary black hole coalescence.
We obtain these echoes by solving the Teukolsky equation for the $\psi_4$
associated with gravitational waves that propagate toward the horizon of a Kerr
spacetime, and process the subsequent reflections of the horizon-going wave by
the surface of the ECO, which lies right above the Kerr horizon. The
trajectories of the infalling objects are modified from Kerr geodesics, such
that the gravitational waves propagating toward future null infinity match
those from merging black holes with comparable masses. In this way, the
corresponding echoes approximate to those from comparable-mass mergers. For
boundary conditions at the ECO surface, we adopt recent work using the membrane
paradigm, which relates $\psi_0$ associated with the horizon-going wave and
$\psi_4$ of the wave that leaves the ECO surface. We obtain $\psi_0$ of the
horizon-going wave from $\psi_4$ using the Teukolsky-Starobinsky relation. The
echoes we obtain turn out to be significantly weaker than those from previous
studies that generate echo waveforms by modeling the ringdown part of binary
black hole coalescence waveforms as originating from the past horizon.
