We examine a single diffusion flame anchored to 1/4-spaces of solid fuel and oxidizer, a configuration relevant to the combustion of heterogeneous solid propellants. A time-periodic shear flow is applied, to model the shear that can be generated by the interaction of acoustic waves and the rotational base flow in a rocket chamber. The response of the flame to this shear, the heat flux to the surface, etc., are calculated numerically. Significant enhancement of the maximum temperature and the time-averaged total heat flux to the surface are found. These enhancements are essentially maximized at zero frequency, and at low frequencies the response depends critically on the instantaneous direction of the shear.