The locking-on of the duct acoustic frequency to the natural vortex shedding frequency of a reacting flow in a backward-facing step combustor is demonstrated using a reduced-order model. All three participating process – flow, combustion and acoustics are individually formulated. A two-dimensional flow field is presented using a potential flow model of the step geometry. Velocity profiles in the resulting time-averaged recirculation zone closely resemble -like profiles characteristic of flows past a step. The flow model captures an increase in the vortex circulation upon strong acoustic forcing resembling large-scale vortex roll-up, a key component in the lock-on mechanism. A modulation of the heat release rate fluctuations is enabled by vortices advecting past the flame, overcoming the time- and space-localised assumptions in vortex kicked-oscillator models. A sweep of the Reynolds number reveals a series of mode transitions of the acoustic pressure , the most significant of which is a locking on of the duct acoustic mode to the vortex shedding mode, during which a nonlinear rise in amplitude is captured. These results compare well with experimental trends across similar operating conditions. A framework for linear global stability analysis is also sought to predict the competing contributions of the acoustic coupling terms over a range of flow parameters. A shift of the stability boundaries in the parameter space as a result of such an analysis with a change in the acoustic forcing amplitudes is also prominently noted.