Smoking flares represent visual evidence of atmospheric emissions from industrial plants, so smoke suppression has become an important issue of public concern. Current environmental regulations limit the amount of time a flare can smoke. Steam-assisted and air-assisted flares are designed to provide smokeless combustion by adding steam or air into the combustion zone, which promote turbulence for mixing and educt more air into the flame. In addition, the injection of steam also presents beneficial chemistry interactions with carbon particles. On the other hand, experimental studies have shown that an excess of steam or air can dramatically reduce the flare efficiency, leading to large emissions of highly reactive volatile organic compounds. This investigation is intended to improve understanding of the thermochemistry effects of steam and air addition on the combustion efficiency of industrial flares. For this purpose, we have utilized Fluent 6.2 to predict the combustion efficiency for different steam/fuel and air/fuel ratios on a set of turbulent non-premixed flames. On the basis of this analysis, mitigation strategies to reduce hydrocarbon emissions for flares can be developed in the future.