Poorly understood "baryonic physics" impacts our ability to predict the power spectrum of the kinetic Sunyaev- Zel'dovich (kSZ) effect. We study this in a sample high-resolution simulation of galaxy formation and feedback, Illustris. The high resolution of Illustris allows us to probe the kSZ power spectrum on multipoles l = 103-3 104. Strong AGN feedback in Illustris nearly wipes out gas fluctuations at k 1 h Mpc-1 and at late times, likely somewhat underpredicting the kSZ power generated at z 1. The post-reionization kSZ power spectrum for Illustris is well-fit by < = 1.38 mK z 6 0.21 2 over 3000 10,000, somewhat lower than most other reported values but consistent with the analysis of Shaw et al. Our analysis of the bias of free electrons reveals subtle effects associated with the multi-phase gas physics and stellar fractions that affect even linear scales. In particular, there are fewer electrons in biased galaxies, due to gas-cooling and star formation, and this leads to an electron bias of less than one, even at low wavenumbers. The combination of bias and electron fraction that determines the overall suppression is relatively constant, f b ∼ 0.7 e e 2 0 2 , but more simulations are needed to see if this is Illustris-specific. By separating the kSZ power into different terms, we find that at least 6% (10%) of the signal at =3000 (10,000) comes from non-Gaussian connected four-point density and velocity correlations, ádvdvñc, even without correcting for the Illustris simulation box-size. A challenge going forward will be accurately modeling long-wave velocity modes simultaneously with Illustris-like high resolution to capture the complexities of galaxy formation and its correlations with large-scale flows.