Pressure-driven Molecular Dynamics simulations were employed to examine reverse osmosis desalination through graphene-oxide-based multilayered membranes. The effects of functionalization of the graphene-oxide flakes with poly(ethylene imine) branches in water permeability and salt rejection were described in detail. The role of the degree of structural rigidity of the membranes was also explored. A lower degree of rigidity of the membrane resulted in a 6–9 % increase in water permeability depending on the state of functionalization of the flakes. At constant membrane rigidity, functionalization of the membranes’ flakes led to approximately 30 % reduction in water permeability, but the water flux remained 2–3 orders of magnitude higher than that of conventional reverse-osmosis membranes. Moreover, functionalization of the membranes’ flakes resulted in a higher than 20 % enhancement in salt rejection at a pressure difference similar to that in actual reverse osmosis processes. Examination of the swelling behavior of the membranes showed that those based on the functionalized flakes exhibit a tendency to remain structurally coherent with an interlayer separation determined by the presence of the polymer branches. Description of the microscopic mechanisms related to the membranes’ water and ion flux, such as hydrogen bonding and concentration polarization, allowed the assessment of the contribution of different factors involved in desalination, providing new insight towards the fabrication of membranes with improved performance.