  Gravitational-wave echoes in the post-merger signal of a binary coalescence
are predicted in various scenarios, including near-horizon quantum structures,
exotic states of matter in ultracompact stars, and certain deviations from
general relativity. The amplitude and frequency of each echo is modulated by
the photon-sphere barrier of the remnant, which acts as a spin- and
frequency-dependent high-pass filter, decreasing the frequency content of each
subsequent echo. Furthermore, a major fraction of the energy of the echo signal
is contained in low-frequency resonances corresponding to the quasi-normal
modes of the remnant. Motivated by these features, in this work we provide an
analytical gravitational-wave template in the low-frequency approximation
describing the post-merger ringdown and the echo signal of a spinning
ultracompact object. Besides the standard ringdown parameters, the template is
parametrized in terms of only two physical quantities: the reflectivity
coefficient and the compactness of the remnant. We discuss novel effects
related to the spin and to the complex reflectivity, such as a more involved
modulation of subsequent echoes, the mixing of two polarizations, and the
ergoregion instability in case of perfectly-reflecting spinning remnants.
Finally, we compute the errors in the estimation of the template parameters
with current and future gravitational-wave detectors using a Fisher matrix
framework. Our analysis suggests that models with almost perfect reflectivity
can be excluded/detected with current instruments, whereas probing values of
the reflectivity smaller than $80\%$ at $3\sigma$ confidence level requires
future detectors (Einstein Telescope, Cosmic Explorer, LISA). The template
developed in this work can be easily implemented to perform a matched-filter
based search for echoes and to constrain models of exotic compact objects.
