We map the distribution and kinematics of the stellar and warm molecular gas within the central 500 parsecs in the Keck OSIRIS Nearby AGN (KONA) survey of 40 local, representative AGN. The observed stellar velocity fields for most galaxies are well reproduced by a rotating disk model, and the best fit kinematic position angle for these disks are found to be consistent with the large-scale photometric position angle of the host galaxy. The observed molecular gas, traced by H2 2.12 microns, is also well fit by a rotating disk model. While the dominant kinematic component is typically disk rotation, kinematic evidence of both inflow and outflow in the molecular gas is also present in many cases. The molecular gas emission follows a similar radial distribution as the stars, but half of the sample shows misalignment of the kinematic position angle for the molecular gas and stellar disks. The residual gas velocities are found to correlate with the hard X-ray luminosity for both the stellar and molecular gas components, suggesting a greater AGN influence on the circumnuclear region in more luminous AGN.