This paper describes a spatial direct numerical simulation (DNS) of the flow transition of a buoyant diffusion flame established on a rectangular nozzle with an aspect ratio of 2:1. Combustion is represented by a one-step finite-rate Arrhenius chemistry. Without applying external perturbations, large vertical structures develop naturally in the flow field due to buoyancy effects. The vortex dynamics of the rectangular buoyant reacting jet has been analysed. The interaction between density gradients and gravity initiates the flow vorticity in the cross-streamwise directions. The streamwise vorticity is mainly generated by the vortex stretching. Downstream of the reacting jet, a more disorganized flow regime characterized by small scales has been observed, following the breakdown of the large vortical structures due to three-dimensional vortex interactions. Analysis of the energy spectra shows that the spatially developing reacting jet has a tendency of transition to turbulence under the effects of combustion-induced buoyancy. Buoyancy effects are found to be very important to the formation, development, interaction and breakdown of vortices. In contrast with the relaminarization effects of chemical exothermicity on non-buoyant jet diffusion flames via volumetric expansion and viscous damping, the tendency towards transition to turbulence in buoyant reacting jets is greatly enhanced by the overwhelming buoyancy effects. Calculations of the mean flow property show that the rectangular buoyant reacting jet has a higher entrainment rate than its non-reacting counterpart.