In this study, machine learning algorithms are employed to calculate state-to-state transport coefficients in nonequilibrium reacting gas flows. The focus is on the evaluation of thermal conductivity, shear viscosity, and bulk viscosity coefficients under conditions of strong coupling between vibrational-chemical kinetics and gas dynamics. In order to solve a regression problem for evaluating state-to-state transport coefficients, a specific software application with user interface is developed, which allows loading, processing, and saving of data arrays; configuring model architecture; training and evaluating models with various optimizers, loss functions, and metrics; making predictions using trained models. Using the developed software the multi-layer perceptron regression model is constructed and trained. The model is assessed in a binary mixture of molecular and atomic nitrogen taking into account 48 vibrational states; the coefficients are computed in the wide temperature range for the varying mixture composition. Good agreement of the results with the original transport coefficients calculated using rigorous but computationally expensive kinetic theory algorithms is shown. Applying machine learning techniques yields a significant speedup of about two orders of magnitude in the computation of transport coefficients. It is concluded that implementation of machine learning methods may considerably reduce the computational efforts required for nonequilibrium flow simulations.