In this paper, we consider the problems of combustion of a foamed emulsion consisting of oxygen bubbles dispersed in the emulsion, which represents a water solution of surfactant with oil drops distributed in it. The interest to study such problems is caused by the perspective of obtaining a new type of fuel based on a water oil blend as well as by the need to solve ecological issues related to oil spilled on the water surface. At a significant content of water in the combustible foam, an irregular regime of flame propagation can be established that is related to sequential quenching and reignition of the foam. On the basis of experimental research, we study the influence of the magnesium oxide particle fraction, fuel concentration, and tube diameter on the speed of flame propagation in the foamed emulsion in the quenching/reignition regime. It is found that the presence of magnesium oxide particles in the foam leads to an increase in the total burning rate of the foam. A reduction in the tube diameter and the use of a leaner foam favor the onset of the quenching/reignition regime.