Polymer layered silicates form an important class of nanocomposite materials. These structures may be formed by annealing layered silicate particles, whose surfaces have been chemically modified to render them organophilic, with a polymer melt. During intercalation, polymer molecules leave the bulk melt and enter the galleries between the silicate layers. An essential feature of this process is the flow of macromolecules from a bulk fluid to a confined environment. To model this phenomenon, we have performed molecular-dynamics simulations of the flow of polymer molecules from a bulk melt into a rectangular slit. The simulations are consistent with a diffusive description of the transport, and show qualitative agreement with time-dependent x-ray diffraction measurements of intercalation kinetics in layered nanocomposites.