We consider a simple model for steady-state luminescence of single polymer chains in a dilute solution in the case when excitation quenching is due to energy transfer between a donor and an acceptor attached to the ends of the chain. We present numerical results for Rouse chains without or with hydrodynamic interactions, which are taken into account in a perturbative manner. We consider the situations of a quiescent solvent as well as the chain in a shear flow and discuss the dependence of the steady-state luminescence intensity on the strength of hydrodynamic interaction and on the shear rate in the flow.