In this work, the process for obtaining aluminum nitride in the combustion mode of co-flow filtration of a nitrogen–argon mixture was investigated. The combustion of granules consisting of aluminum and aluminum nitride as an inert diluent was studied under conditions of co-current filtration in a flow of nitrogen and a nitrogen–argon mixture in the range of a specific flow rate of 1.5–5.0 cm3/(s∙cm2). It was found that the specific flow rate of the gas mixture and the amount of argon in the nitrogen–argon mixture had a significant effect on the rate and the temperature of combustion. The structure and phase composition of the synthesis products were studied. The maximum achieved yield of the AlN phase was 95 wt.%. Moreover, this method is energy efficient and allows the production of metal nitrides without the use of high-pressure reactors.