The force exerted on a material by an incident beam of light is dependent upon the material's velocity in the laboratory frame of reference. This velocity dependence is known to be diffcult to measure, as it is proportional to the incident optical power multiplied by the ratio of the material velocity to the speed of light. Here we show that this typically tiny effect is greatly amplified in multilayer systems composed of resonantly absorbing atoms (e.g. optically trapped 87Rb), which may exhibit ultra-narrow photonic band gaps. The amplification of the effect is shown to be three orders of magnitude greater than previous estimates for conventional photonic-band-gap materials, and significant for material velocities of a few ms/s.