Aggregation and flow of polymer chains (each of length L-c) on a heterogeneous surface are studied in presence of a field E using a hybrid simulation. Effects of field, heterogeneity (i.e., the barrier concentration p(b)), and temperature T on aggregation and desegregation of chains with low molecular weight is found to be different from that with high molecular weight. For low L-c, at low T = 0.2, the impurity barriers act as seeds for pinning the growth of molecular aggregates that lead to larger aggregates at lower p(b). At high temperature (T = 1.0), in contrast, larger aggregates appear at higher p(b) where pinning of aggregates is augmented by cluster of clustering. For large L-c, orientational ordering with a molecular bridging occurs at low p(b), while a nearly isotropic network of chains anchored by the barriers emerges at higher p(b). The rms displacement of chain ranges from drift-like for short chains at low barrier concentration to strongly subdiffusive for long chains at high fields. A linear response of the flow rate density j to field j similar to E is observed over low to moderate fields (E less than or equal to 1.0), high temperature (T greater than or equal to 1), and low barrier concentrations (p(b) less than or equal to 0.1). The variation of the effective linear permeability phi(m) of polymer with the field is nonmonotonic over the range 0.0 < E < 1.0, with decreasing trend at higher values of E. In the low field regime (E < 0.2), the monomer permeability shows a power-law decrease with chain length phi(m) similar to L-c(-alpha), alpha similar or equal to 0.25-0.37.