The predictive capability of third-order Extended Thermodynamics (ET3) models for chemically reactive nonequilibrium flows depends critically on the accurate estimation of transport coefficients governing higher-order relaxation processes. These coefficients, including higher-order viscosities, thermal conductivities, relaxation times, and nonlinear coupling parameters, are often difficult to determine experimentally and remain a significant source of model uncertainty. This paper presents a Bayesian inference framework for the estimation and uncertainty quantification of third-order transport coefficients in reactive nonequilibrium flows. The proposed methodology combines the ET3 governing equations with a probabilistic inverse modelling approach that incorporates experimental measurements and high-fidelity numerical data through Bayes’ theorem. Prior distributions are assigned to the unknown transport parameters based on physical constraints and kinetic-theory considerations, while posterior distributions are obtained using Markov Chain Monte Carlo (MCMC) sampling. Model predictions are accelerated through surrogate modelling techniques, enabling efficient exploration of high-dimensional parameter spaces without compromising predictive accuracy. Posterior uncertainty is propagated through the governing equations to quantify confidence intervals for macroscopic observables, including temperature, pressure, species concentrations, heat flux, higher-order moments, and entropy production. Global sensitivity analysis is performed to identify the dominant transport coefficients influencing reactive shock structures and nonequilibrium relaxation processes. Synthetic benchmark problems demonstrate that Bayesian calibration substantially reduces parameter uncertainty while improving agreement between theoretical predictions and reference solutions. The resulting posterior distributions provide physically interpretable estimates of higher-order transport properties together with rigorous credibility intervals, thereby enhancing the robustness and predictive capability of third-order Extended Thermodynamics models. The proposed framework establishes a systematic methodology for integrating thermodynamic theory, statistical inference, and uncertainty quantification, providing a foundation for data-informed modelling of chemically reacting nonequilibrium flows in combustion, hypersonic aerothermodynamics, plasma physics, and high-energy-density applications.