We analyse the enhanced flow rate of water through nano-fabricated graphene channels that has been recently observed experimentally. Using molecular dynamics simulations in channels of similar lateral dimensions as the experimental ones, our results reveal for the first time a relationship between water structure and the variation of flux in the rectangular graphene channels. The substantial enhancement in the flow rate compared to Poieseuille flow is due to the formation of layered 2D structures in the confined space, which persists up to a channel height of 2.38 nm, corresponding to six graphene layers. The structure of the water shows an intricate crystal of pentagonal and square tiles, which has not been observed before. Beyond six layers we find a sudden drop in flux due to the disordering of the water, which obeys classical flow dynamics.