The electrokinetic transport of fluids, also called the electroosmotic flow (EOF), in micro/nanoscale devices occurs in promising applications such as electrokinetic energy conversion (EKEC) systems. Recently, EKEC systems grafted with end-charged polyelectrolyte (PE) layers (PELs) have been reported to exhibit higher efficiencies than those of intrinsic systems. Understanding the interplay between the end-charged PELs and electrical double layers (EDLs) on the EOF is crucial for designing highly efficient EKEC systems. The interplay between the end-charged PELs and EDLs on the strength of the EOF (V 0) is studied by explicitly modeling the EOF through nanochannels grafted with end-charged PELs using atomic simulations. The variation of V 0 is examined for nanochannels grafted with PELs at various separations (d = 3.5-0.4 nm) to cover various conformations of PEs, inlcuding mushroom, semi-dilute brushes, and concentrated brushes. We find that V 0 follows a non-monotonic variation as d decreases and this is correlated with the conformation of the PEs. Specifically, as d decreases, V 0 decreases first in the mushroom regime (d = 3.5-2.0 nm), and then V 0 increases in the concentrated brush regime (d = 0.75-0.4 nm). Navigated by the continuum Navier-Stokes-Brinkman model, the above observations are rationalized by the competition between the driving effect from the spatial shift of ions in EDLs and the drag effect from PELs. The insights obtained in this work are important to guide the design of highly efficient EKEC systems by grafting end-charged PELs onto channel surfaces.