Biomass thermal conversion is one of the promising methods for cleaner heat energy production. Different factors (in particular, rotation of the boundary) can affect energy conversion process. In the present study, we investigate the effect of rotation of the boundaries on the stability of a convective flow in a vertical annulus caused by nonlinear heat sources due to chemical reaction that takes place in the fluid. The base flow is described by a nonlinear boundary value problem (BVP). It is proved that depending on the values of the parameters, there exist two or one positive solutions of the BVP, or the problem has no positive solution. In addition, the estimates for the norm of the solutions are obtained. The analysis conducted in the study allows one to select the correct solution for linear stability analysis. The solution with the smallest norm should be selected since the other solution is linearly unstable with respect to small perturbations (and, therefore, cannot be observed in the laboratory). Linear stability problem with respect to axisymmetric perturbations is solved numerically using collocation method. Calculations show that there are several factors that destabilize the flow (increase of the angular velocity of rotation of the boundaries, thermal effect of the chemical reaction, and the Prandtl number of the fluid). Weakly nonlinear analysis of the flow above the threshold is performed. It is shown that the amplitude evolution equation for the most unstable mode is the complex Ginzburg-Landau equation. The results of the study can be used for design of bioreactor systems.