We perform molecular dynamics simulations to investigate the shear dynamics of hydration water nanoconfined between two mica surfaces at 1 bar pressure and 298 K. Newtonian plateaus of shear viscosity comparable to the bulk value for different hydration layers D=0.92-2.44 nm are obtained. The origin of this persistent fluidity of the confined aqueous system is found to be closely associated with the rotational dynamics of water molecules, accompanied by fast translational diffusion under this confinement.