  In this work we study propagation of chaos for solutions of the Liouville
equation for the classical discrete Cucker-Smale system. Assuming that the
communication kernel satisfies the heavy tail condition -- known to be
necessary to induce exponential alignment -- we obtain a linear in time
convergence rate of the $k$-th marginals $f^{(k)}$ to the product of $k$
solutions of the corresponding Vlasov-Alignment equation, $f^{\otimes k}$.
Specifically, the following estimate holds in terms of Wasserstein-2 metric
\begin{equation}\label{e:abst}
  \mathcal{W}_2(f^{(k)}_t,f^{\otimes k}_t) \leq C k^{1/2} \min\left\{ 1,
\frac{t}{\sqrt{N}} \right\}. \end{equation} For systems with the Rayleigh-type
friction and self-propulsion force, we obtain a similar result for sectorial
solutions. Such solutions are known to align exponentially fast via the method
of Grassmannian reduction, \cite{LRS-friction}. We recast the method in the
kinetic settings and show that the bound \eqref{e:abst} persists but with the
quadratic dependence on time.
  In both the forceless and forced cases, the result represents an improvement
over the exponential bounds established earlier in the work of Natalini and
Paul, \cite{NP2021-orig}, although those bounds hold for general kernels. The
main message of our work is that flocking dynamics improves the rate
considerably.
