Stochastic resonance (SR) is demonstrated under two-parameter modulation in a model of the photosensitive Belousov-Zhabotinsky reaction in a flow system. Light flux and a flow rate are two control parameters in the model, and modulate a focal steady state close to a Hopf bifurcation simultaneously. Addition of noise to the light flux gives rise to SR whose behavior depends on the periods of and phase difference in the two modulations. Compared with one-parameter modulation by the light flux, the additional flow rate modulation results in both increase and decrease in the resonance, strong resonance with a period different from that of a signal, or suppressed resonance. These computational results are interpreted by a threshold scenario of SR applied to the two-parameter system. The effect of the flow rate modulation on SR in the photosensitive system is also studied from the viewpoint of the peristaltic effect of a pump.