  We use the frequency and time domain Teukolsky formalism to calculate
gravitational-wave fluxes from a spinning body on a bound eccentric equatorial
orbit around a Kerr black hole. The spinning body is represented as a point
particle following the pole-dipole approximation of the
Mathisson-Papapetrou-Dixon equations. Reformulating these equations we are not
only able to find the trajectory of a spinning particle in terms of its
constants of motion, but also to provide a method to calculate the azimuthal
and the radial frequency of this trajectory. Using these orbital quantities, we
introduce the machinery to calculate through the frequency domain Teukolsky
formalism the energy and the angular momentum fluxes at infinity, and at the
horizon, along with the gravitational strain at infinity. We crosscheck the
results obtained from the frequency domain approach with the results obtained
from a time domain Teukolsky equation solver called Teukode.
