We present results from XRISM/Resolve observations of the core of the galaxy cluster Abell 2319, focusing on its kinematic properties. The intracluster medium (ICM) exhibits temperatures of approximately 8 keV across the core, with a prominent cold front and a high-temperature region ($\sim$11 keV) in the northwest. The average gas velocity in the 3 arcmin $\times$ 4 arcmin region around the brightest cluster galaxy (BCG) covered by two Resolve pointings is consistent with that of the BCG to within 40 km s$^{-1}$ and we found modest average velocity dispersion of 230-250 km s$^{-1}$. On the other hand, spatially-resolved spectroscopy reveals interesting variations. A blueshift of up to $\sim$230 km s$^{-1}$ is observed around the east edge of the cold front, where the gas with the lowest specific entropy is found. The region further south inside the cold front shows only a small velocity difference from the BCG; however, its velocity dispersion is enhanced to 400 km s$^{-1}$, implying the development of turbulence. These characteristics indicate that we are observing sloshing motion with some inclination angle following BCG and that gas phases with different specific entropy participate in sloshing with their own velocities, as expected from simulations. No significant evidence for a high-redshift ICM component associated with the subcluster Abell 2319B was found in the region covered by the current Resolve pointings. These results highlight the importance of sloshing and turbulence in shaping the internal structure of Abell 2319. Further deep observations are necessary to better understand the mixing and turbulent processes within the cluster.