A previously introduced degenerate diffusion-reaction model of biofilm growth and disinfection is extended to account for convective transport of oxygen and disinfectants in an aqueous environment. To achieve this in a computationally efficient manner we employ a thin-film approximation to the (Navier)-Stokes equations that can be solved analytically. In numerical experiments, we investigate how the convective transport of nutrients and disinfectants due to bulk flow hydrodynamics affects the balance between growth and disinfection processes. It is found that the development of biofilms can be significantly affected by the flow field even at extremely low Reynolds numbers. While it is natural to expect that increased bulk flow velocities imply increased mass transfer of both, nutrients and disinfectants, and hence an acceleration of both, growth and decay of biomass, it is found, furthermore, that in many instances the actual flow conditions, determine the success or failure of disinfection, i.e. persistence or extinction of a biofilm community.