For volumetric reconstruction of the refractive index field in a flow, background-oriented schlieren (BOS) imaging which measures the deflection of light rays due to refractive index variations is combined with an evolutionary tomographic algorithm for the first time, called evolutionary BOS tomography (EBOST). In this work application to reactive flows is presented. Direct non-linear ray-tracing of the reconstruction domain is used to evaluate the fitness of solution candidates during the evolutionary strategy that was implemented to run on a multi-GPU system. The use of a diversity measure and its consideration in a migration policy was tested against a simple scheme that distributes the best chromosome (solution candidate) in an island-based genetic algorithm. The extensive set of control parameters of the presented algorithm was harnessed by a self-adaptive strategy taking into account the fitness function and operator rates. Quantitative characterisation of the EBOST via numerical phantom studies, using flame simulations as ground truth data is presented. A direct comparison to a state-of-the-art BOST algorithm demonstrates similar accuracy for a turbulent swirl flame phantom reconstruction. A series of experimental applications of the EBOST on several unsteady and turbulent flames is also presented. In all cases, the instantaneous and time-averaged flame structure is revealed, proving the benefit of EBOST for volumetric flow diagnostics.