  We consider the covariant proposal for the gravitational Compton amplitude
for a Kerr black hole. Employing the covariant three- and four-point Compton
amplitudes, we assemble the classical one-loop integrand on the maximal cut at
all orders in spin, utilizing the method of unitarity. Expanding in powers of
spin, we evaluate the one-loop amplitude up to $\mathcal O(G^2 a^8)$.
Supplemented with extra contact contributions derived from the far-zone data of
the Teukolsky solutions, the one-loop amplitude is in agreement with results
available in the literature. We showcase the classical eikonal in the
aligned-spin case at $\mathcal O(G^2 a^7)$.
