The paper presents the results of an experimental study of the combustion process of fuel gases mixed with hydrogen in jet-niche flame stabilizer (JNS). The study of the flare structure hydrodynamics shows a significant effect of the hydrogen addition, which is accompanied by an intensification of the chemical reaction process. The hydrogen admixture increment by more than 30% by volume leads to the rearrangement of the reacting mixture flow in the flame stabilization zone, which is accompanied by the degeneration of the vortex structure behind the stabilizer’s breaking edge and the transfer of the stabilization zone to the gas supply holes. It was determined that in an open flame, the temperature increases by 35…40 °C at the burner mouth, when hydrogen is added to more than 50%, and by 100–120 °C for pure hydrogen compared to natural gas. The measurements results showed that for a mixture with the 50% hydrogen addition, the limit of “poor” disruption according to the excess air coefficient shifts by more than 2 times, and for a 70% mixture—by more than three times. It was established that the minimum power for a 50/50 mixture is reduced by 60%, which increases the operating regulation factor by 2.5 times up to 12.5 for a stabilizer in this configuration with a 50 kW nominal power. The nitrogen oxides emission increases, when H2 is added, and depends on the stabilizer power and its operation mode. The maximum growth of NOx concentrations for the mixture occurs in combustion conditions close to “stoichiometric” and is 65% compared to burning natural gas. The burner power increment from 20 to 30 kW leads to a relatively smaller increase in the harmful gases emission and reaches 20%. It is also determined that the intensification of mixed fuels combustion processes is manifested in the carbon combustion improvement in the entire range of operating modes, especially the decrease of CO concentrations is observed for natural gas with hydrogen in the lean combustion zone (α > αcr2 = 1.5). Thus, for a natural gas mixture with H2, CO decreases more than 10 times (to 27 ppm) in the α = 2.0 area. According to the measurements results of CO2 emissions when burning natural gas, the reduction of carbon dioxide emissions is 24.0% in the case of replacing natural gas with 50% hydrogen by volume. These results are confirmed by theoretical calculations.