This study presents a self-consistent framework for deriving slip boundary conditions within multitemperature modeling of non-equilibrium reacting gas mixture flows. The framework is based on a previously developed method using the kinetic boundary condition, extended to account correctly for particle loss due to adsorption, desorption, and surface chemical reactions. Relations for velocity slip, translational-rotational temperature jump (TJ), and vibrational TJs are derived without additional phenomenological assumptions under the specular-diffusive scattering model. These conditions simultaneously account for gas-surface scattering effects and heterogeneous processes, including rotational and vibrational relaxation. A solver is developed to compute the resulting nonlinear system, with recommendations provided for integration into fluid dynamic codes. Parametric studies of TJs, relative changes in mixture composition, and surface heat flux are carried out by varying the recombination probability on the surface, accommodation coefficient, wall temperature, and Knudsen number. It is demonstrated that vibrational TJs are critical for predicting near-wall flow properties, and that rotational relaxation significantly affects the TJ, especially when there is a large temperature difference between the gas phase and the wall. The framework enables accurate modeling of non-equilibrium gas flows near surfaces in both continuum and slip-flow regimes.