  In this work, by using the Malliavin calculus, under H\"ormander's condition,
we prove the existence of distributional densities for the solutions of
stochastic differential equations driven by degenerate subordinated Brownian
motions. Moreover, in a special degenerate case, we also obtain the smoothness
of the density. In particular, we obtain the existence of smooth heat kernels
for the following fractional kinetic Fokker-Planck (nonlocal) operator:
\[\mathscr{L}^{(\alpha)}_b:=\Delta^{\alpha/2}_{\mathrm{v}}+\mathrm {v}\cdot
\nabla_x+b(x,\mathrm{v})\cdot \nabla_{\mathrm{v}},\qquad
x,\mathrm{v}\in\mathbb{R}^d,\] where $\alpha\in(0,2)$ and
$b:\mathbb{R}^d\times\mathbb{R}^d\to \mathbb{R}^d$ is smooth and has bounded
derivatives of all orders.
