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.