Advanced batteries are required for an optimal use of intermittent renewable energy sources and to boost new global energy policies. Flow lithium oxygen batteries represent a cutting-edge technology that brings in a unique solution the advantages of the high specific energy of Li/O2 batteries and the design flexibility of redox flow batteries. To maximize the performance of flow lithium oxygen batteries, a careful study of the fluid dynamics of the flow frame of the cell is still needed. Indeed, the pressure drops through the cell generate a loss of power that has to be minimized by a smart cell design. For the first time, the experimental evaluation and the modeling of the power balance of laboratory prototypes of flow lithium oxygen battery cells is here reported. We propose a new, simple semi-empirical approach provides a general law of the net power output of the cell vs flow velocity. We demonstrate that by an intelligent cell geometry it is possible to drastically reduce pressure drops even with viscous systems like the organic electrolytes used in high specific energy batteries. This novel semi-empirical approach can accelerate prototyping of advanced flow redox batteries.