Vigorous burning of vortices, formed behind flame stabilizers, can drive significant pressure oscillations inside premixed-type combustors. The goal of this work is to derive a reduced-order model for interaction among vortex shedding, chamber acoustics, and combustion process. A dump combustor is considered a general system configuration. Formation of vortices at the sudden expansion in a chamber is affected by the oscillatory flow. A new quasi-steady model is proposed for determining the moment of vortex separation. Vortex burning is assumed to be localized in space and time. A "kicked'' oscillator model is utilized for deriving the appropriate dynamical system. The moment of burning and the corresponding vortex location are dependent on the chamber geometry, velocity field, and characteristic chemical and hydrodynamic times. If Rayleigh's criterion is satisfied, acoustic waves can develop in the chamber. Model and experimental results are compared for a chosen configuration. A study of model performance for a realistic system is carried out by variation of parameters where the mean flow velocity and the number of modes are treated as variables.