Prediction of pollutant emissions is a key aspect of modern combustor design in energy conversion systems. In the presented work, a simple and robust model based on low-order reaction networks is applied to a FLOX® laboratory combustor at atmospheric conditions. The applied approach is computationally cheap and therefore highly suited for design studies. Steady-state CFD RANS simulations are carried out, serving as a basis for the network generation algorithm. CFD results are validated with experimental data for flow field and combustion. Different degrees of fidelity of reactor network models are taken into consideration and findings are opposed to measurements, evaluating the quality of the low-fidelity models. Validation of CO and NOx emission results of reactor network modeling provides accurate qualitative and quantitative reproduction of experimental findings, depending on the degree of heat loss applied on the combustion system. The introduced approach is therefore readily applicable to large-scale, industrial, and gas turbine combustion.