We extend the theoretical framework of de Gennes for treating diffusion-controlled reactions in complex fluid systems to situations in which a steady, linear flow is externally imposed. Consideration is restricted to systems that are dilute in reactive sites and for which the reaction occurs instantaneously and irreversibly when a pair of sites are brought in close contact. Illustrative calculations are presented for the long-time intermolecular trapping rate constant in polymer melts where a small fraction of chains have a single terminally attached reactive group. Both shear and extensional flows are considered, as well as Rouse and reptation models of chain dynamics. Extensions of the analysis may have applications in modeling free radical termination processes and reactive blending.