  We derive quantitatively the Harnack inequalities for kinetic
integro-differential equations. This implies H\"older continuity. Our method is
based on trajectories and exploits a term arising due to the non-locality in
the energy estimate. This permits to quantitatively prove the intermediate
value lemma for the full range of non-locality parameter $s \in (0, 1)$. Our
results recover the results from Imbert and Silvestre [22] for the
inhomogeneous Boltzmann equation in the non-cutoff case. The paper is
self-contained.
