Polymer layered silicates form an important class of nanocomposite materials. During their formation by melt intercalation, polymer molecules from a bulk fluid move into the galleries of layered silicates. 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.