Diffusioosmosis refers to the deterministic fluid motion over a surface induced by a solute concentration gradient. Existing models can predict separately the effects of surface hydrophobic slip and electrolyte ion-ion electrostatic correlations on diffusioosmosis. A predictive model for the coupled dynamics of hydrodynamic slip and electrostatic correlations in diffusioosmosis is lacking. Here, we develop a mathematical framework to simulate the diffusioosmosis of an electrolyte in a hydrophobic channel. We analyze how the surface properties of the channel, ion-ion interactions, and the electrolyte concentration affect the diffusioosmotic flow. The present model can be used to understand and predict diffusioosmosis in a wide range of applications, including enhanced oil recovery, nanoparticle drug delivery, and colloidal species separation.