The electroosmosis of multivalent electrolytes through hydrophobic channels are commonly modeled through a mean-field based approach and imposing the Navier-slip condition at the charged surface. However, the surface charge at the hydrophobic interface are laterally mobile, creating frictional force as well as electric force to the adjacent fluid and thus, modify the slip condition and influence the ion transport. The slip velocity condition at the interface is developed based on the balance of hydrodynamic and electric forces on the surface ions. Electrokinetics involving multi- valent counterions manifest the strong coupling among ions, ceasing the validity of the mean-field based ion transport. The ion-ion correlations among the finite-sized ions are modeled based on the nonlocal electrostatic consideration. The governing equations are solved numerically to elucidate the interactions of surface charge with its hydrophobicity as well as the short-range effects on ion transport. A simplified model is also developed under the assumption of a small Debye length-to- channel height ratio, which is further solved analytically based on a linearized approximation. At the non-dilute situation the short-range effects such as, ion steric interactions and ion-ion correla- tions manifest. Our results show that the ionic correlations induced counterion condensed layer can overscreen the surface charge and creates a inversion in charge density, leading to a reversal in the electroosmosis. This counterion condensed layer diffuses at a higher ionic concentration when sur- face charge density becomes sufficiently large. The occurrence of velocity slip at the wall defers the charge density inversion and consequently, electroosmotic flow reversal, by enhancing momentum transfer to the fluid. The intensity of the slip attenuates when the surface charge is considered to be laterally mobile.