  We calculate the second order viscous correction to the kinetic distribution,
$\delta f_{(2)}$, and use this result in a hydrodynamic simulation of heavy ion
collisions to determine the complete second order correction to the harmonic
spectrum, $v_n$. At leading order in a conformal fluid, the first viscous
correction is determined by one scalar function, $\chi_{0p}$. One moment of
this scalar function is constrained by the shear viscosity. At second order in
a conformal fluid, we find that $\delta f(\p)$ can be characterized by two
scalar functions of momentum, $\chi_{1p}$ and $\chi_{2p}$. The momentum
dependence of these functions is largely determined by the kinematics of the
streaming operator. Again, one moment of these functions is constrained by the
parameters of second order hydrodynamics, $\tau_\pi$ and $\lambda_1$. The
effect of $\delta f_{(2)}$ on the integrated flow is small (up to $v_4$), but
is quite important for the higher harmonics at modestly-large $p_T$. Generally,
$\delta f_{(2)}$ increases the value of $v_n$ at a given $p_T$, and is most
important in small systems.
