Metal air batteries are the promising alternative to power electric vehicles in future. However, they suffer from mass transfer limitations at the higher discharge rates. The use of flow batteries can provide higher specific energies at the higher discharge rates. The flow batteries incorporating sodium as the anode material provides less expensive energy storage option compared to the lithium based flow batteries. In the current study, we focus on the discharge behaviour of the sodium air flow battery. A detailed parametric study is carried out to investigate the influence of the different operating variables such as the discharge current density and the pressure gradient. We identify the distribution of the oxygen concentration through the cell to be the critical parameter relating to the cell performance. Further, we demonstrate that the advantage of using flow configuration compared to the non-flow configuration becomes apparent beyond a critical current density as the parasitic power consumption for obtaining forced convection dominates over the low current density regime. Moreover, the optimal pressure gradient strongly depends on the desired rate of discharge. The inferences presented in the current paper are essential in terms of understanding and designing the futuristic sodium air flow batteries.