Reaction time is defined as a physiological parameter reflecting the period of time between perceiving a stimulus and performing a relevant action. In the traffic flow theory literature, the effects of reaction time on string stability have been described using the microscopic modeling approach. This paper presents a distinct approach to investigate how reaction time influences traffic flow stability using a macroscopic model. In the paper, the distinction between string stability and flow stability is defined. The flow stability conditions are derived based on the macroscopic model, which is developed from a gas-kinetic principle. From linear analysis, we find that at macroscopic scale the reaction time influences how instabilities propagate but does not contribute to whether those (linear) instabilities occur. Nevertheless, nonlinear analysis might give a different view on the impact of reaction time on traffic flow stability, but the effect is nonlinear. We argue that the findings provide a better understanding of the effects of reaction time on traffic flow characteristics.