This paper presents a topology optimization algorithm based on the lattice Boltzmann method coupled with a level-set method for increasing the efficiency of reactive fluid flows. The multi-relaxation time model is considered for the lattice Boltzmann collision operator, allowing higher Reynolds numbers flow simulations compared to the ordinary single-relaxation time model. The cost function gradient is obtained with the derivation of the adjoint-state formulation for the fully coupled problem. The proposed method is tested successfully on several numerical applications involving Reynolds numbers from 10 up to 1,000, as well as with different Damkohler and Peclet numbers. A limitation of the maximal pressure drop is also applied. The obtained results demonstrate that the proposed numerical method is robust and efficient for solving topology optimization problems of reactive fluid flows, in different operating conditions.