Reactions of HBr with radicals are involved in atmospheric chemistry and in the mechanism of operation of bromine-containing flame retardants. The rate coefficients for two such reactions, HBr + OH and HBr + CH₃, are available from earlier experiments at near or below room temperature, relevant for atmospheric chemistry, and in this domain, the activation energy for both has been found to be negative. However, no experimental data are available at combustion temperatures. In this work, to provide reliable data needed for modeling the action of brominated flame suppressants, we used the quasiclassical trajectory (QCT) method in combination with high-level ab initio potential energy surfaces to evaluate the rate coefficients of the two title reactions at combustion temperatures. The QCT calculations have been validated by reproducing the experimental rate coefficients at room temperature. At temperatures between 600 and 3200 K, the QCT rate coefficients display positive activation energies. We recommend the following extended Arrhenius expressions to describe the temperature dependence of the thermal rate coefficients: k₆ = (9.86 ± 2.38) × 10^–16T^(1.23±0.03) exp[(5.93 ± 0.33) kJ mol^–1/RT] cm³ molecule^–1 s^–1 for the HBr + OH → H₂O + Br reaction, and k_–2 = (4.06 ± 2.72) × 10^–18T^(1.83±0.08) exp[(7.53 ± 0.18) kJ mol^–1/RT] cm³ molecule^–1 s^–1 for the HBr + CH₃ → CH₄ + Br reaction. The latter is in very good agreement with the formula proposed by Burgess et al. [Burgess, D. R., Jr.; Babushok, V. I.; Linteris, G. T.; Manion, J. A. A Chemical Kinetic Mechanism for 2-Bromo-3,3,3-trifluoropropene (2-BTP) Flame Inhibition. Int. J. Chem. Kinet. 2015, 47, 533−619, DOI: 10.1002/kin.20923]. The conventional transition state theory has been tested against the rate data obtained by the QCT method and was found to overestimate not only the rate coefficients but also the activation energies