To mitigate its impact on global climate, the power generation sector must strive towards a transition to net-zero emissions of greenhouse gases. This can be achieved by a massive penetration of renewable power generation. However, a high share of renewable power generation requires dispatchable and flexible power generation technologies such as gas turbines to maintain the stability of power grids. To achieve net-zero green house gas emissions, gas turbines have to be operated exclusively with carbon-neutral fuels. Hydrogen is a promising carbon-neutral fuel, although it comes along with several challenges regarding stable combustion. A possible measure to stabilize hydrogen combustion is the partial external recirculation of exhaust gases (EGR). In a previous study, the authors presented a model-based thermodynamic analysis of an industrial gas turbine featuring EGR. The next step was to answer the question of whether the thermodynamically negative impact of EGR (i.e. lower thermal efficiency) is justified by positive effects, such as reduced NOx emissions or a more controllable combustion of hydrogen. By means of a simple 1-D flame approach, the present study provides further insight into the flame behaviour and stability limits during a fuel switch from natural gas to hydrogen. In a following step, the same approach is used to investigate the flame behaviour in an EGR environment at two recirculation temperatures. The results show that if a hydrogen-fired, diffusion-type combustor is combined with sufficiently high EGR ratios, NOx emissions are potentially in the order of a state-of-the-art diffusion-type combustor fired with natural gas. In addition, based on the calculated laminar flame speeds and extinction strain rates, the higher reactivity of hydrogen could potentially be controlled by employing EGR. However, relevant literature suggests that stronger dilution might be required to compensate for the additional impact of turbulence-chemistry interaction in real application which could lead to flame stabilization issues and higher NOx emissions. Moreover, considering the industry efforts to develop hydrogen-capable premixed-type combustors, the results show that EGR has no significantly positive influence on the reactivity of a premixed pure hydrogen flame. The question regarding the preferred EGR temperature is addressed but cannot be answered conclusively.