Kitchen waste and tree branches are two of the most common solid waste materials suitable for on-site disposal. Quantification of combustion characteristics of these waste materials is vital for designing an appropriate incinerator. In this paper, the combustion characteristics of a mixture of kitchen waste and tree branches have been analyzed. As the theoretical basis for the design of incinerator arches is severely limited in the published literature, a novel momentum flux methodology for designing α-shaped flame arches has been developed for the disposal and combustion of two-component solid waste. For this purpose, orthogonal experimental design methodology has been employed for eight different operating conditions of the incinerator. The theoretical results have been verified by cold-state experiments, resulting in the development of a novel small-scale, α-shaped flame incinerator fueled with kitchen waste and tree branches. Cold-state experimental results show that the optimum dimensionless structural parameters of the furnace arches are H1/L of 0.3, H/L of 0.5 and h/L of 0.15, with the front arch angle of 45° and the rear arch angle of 12°. For full-scale validity and commercial viability of the novel incinerator, hot-state tests have been conducted in this study.