In this paper, a method and an effective algorithm for calculating the study of the outflow of a three-dimensional turbulent jet of reacting gases from a rectangular nozzle and propagating in a cocurrent (flooded) air flow are presented. To describe the flow, three-dimensional parabolized systems of Navier-Stokes equations for multicomponent chemically reacting gas mixtures are used. To calculate the turbulent viscosity, a modified model of the first moments of turbulence is proposed, taking into account molecular transfer, three-dimensionality and temperature inhomogeneity of the jet, and a two-parameter "k-ε" turbulence model is used. On the basis of the developed method, the influence of the ratio of the temperature of the combustible jet and the oxidizer, as well as the pressure gradient on the configuration of the diffusion flame, was investigated.