In this article, a new mathematical model is presented that encompasses flame propagation through a two-phase mixture of uniformly distributed organic fuel particles and air. In this analytical study, which is conducted in the framework of a thermal-diffusive model assuming the Lewis number to be varying, and taking into account thermal radiation effect induced from flame front into unburned zone, the flame structure is divided into four integral zones. The system of governing equations is rewritten in the perturbed form with a perturbed flame front, and the time-related solutions are analyzed by using the method of small harmonic perturbations. The main goal of this study is to ascertain to what extent the laws of unsteady conservation damp or amplify the perturbation. As a result, the onset of pulsating instability is computed for both planar and wrinkled dust flames with respect to the variation of wavenumbers, as well as Lewis, Damkohler, and Zeldovich numbers, and also the thermal radiation effect. One of the noticeable results is that the position of pulsating-instability boundary for the flame propagation into the organic dust cloud is strongly affected by the induced thermal radiation, as the onset of pulsating instability under this circumstance becomes more likely. Also, the thermal radiation is an important factor in significantly reducing the frequency of pulsations at the onset of pulsating instability in the combustion of an organic dust-particle cloud.