Electroosmotic flow is one of the most important fluid transport mechanism in nanofluidic systems due to its ease-of-control and excellent scaling behavior. In this paper, we report on the atomistic simulation of electroosmotic flow regulation by coating the channel surface with a thin layer of polymers. While such coating is applied routinely in practice, the fundamental mechanism of the flow control is not well-understood. We show that the flow depends both on the polymer type and coating density. A detailed analysis of these results indicates that the flow regulation has both a hydrodynamic origin and a physio-chemical origin. The results highlight the need to integrate physical chemistry into the fluid mechanics for a fundamental understanding of the fluid transport at nanoscale.