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This work presents a theoretical and numerical study of electrokinetic flow and the zeta potential for the case of slit channels with nanoscale roughness of dimensions comparable to the Debye length, by employing molecular dynamics simulations and continuum-level analyses. A simple analytical model for considering the effects of the surface roughness is proposed by employing matched asymptotic solutions for the charge density and fluid flow field, and matching conditions that satisfy electroneutrality and the Onsager reciprocal relation between the electroosmotic flow rate and streaming current. The proposed analytical model quantitatively accounts for results from molecular dynamics simulations that consider the presence of ion solvation shells and surface hydration layers. Our analysis indicates that a simultaneous knowledge of the electroosmotic and pressure-driven flow rate or streaming current can be instrumental to determine unambiguously the zeta potential and the characteristic surface roughness height.