Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy epsilon between the chaperone and the chain and the chaperone concentration N(s) can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time tau has a transition from a long-tailed distribution to a Gaussian distribution with increasing epsilon. tau rapidly decreases and then almost saturates with increasing binding energy for a short chain; however, it has a minimum for longer chains at a lower chaperone concentration. We also show that tau has a minimum as a function of the chaperone concentration. For different epsilon, a nonuniversal dependence of tau on the chain length N is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either the crowding effect from a high chaperone concentration or the intersegmental binding for the high binding energy.