We consider the flow-driven translocation of single polymer chains through nanochannels. Using analytical calculations based on the de Gennes blob model and mesoscopic numerical simulations, we estimate the threshold flux for the translocation of chains of different number of monomers. The translocation of the chains is controlled by the competition between entropic and hydrodynamic effects, which set a critical penetration length for the chain before it can translocate through the channel. We demonstrate that the polymers show two different translocation regimes depending on how their length under confinement compares to the critical penetration length. For polymer chains longer than the threshold, the translocation process is insensitive to the number of monomers in the chain as predicted in Sakaue et al., Euro. Phys. Lett., 2005, 72, 83. However, for chains shorter than the critical length we show that the translocation process is strongly dependent on the length of the chain. We discuss the possible relevance of our results to biological transport.