Transport properties for collisions of hydrogen atoms with CO and CO2 have been computed by means of quantum scattering calculations. The carbon oxides are important species in hydrocarbon combustion. The following potential energy surfaces (PES's) for the interaction of the molecule fixed in its equilibrium geometry were employed: for H-CO, the PES was taken from the work of Song et al. [J. Phys. Chem. A 117, 7571 (2013)], while the PES for H-CO2 was computed in this study by a restricted coupled cluster method that included single, double, and (perturbatively) triple excitations. The computed transport properties were found to be significantly different from those computed by the conventional approach that employs isotropic Lennard-Jones (12-6) potentials. The effect of using the presently computed accurate transport properties in 1-dimensional combustion simulations of methane-air flames was investigated.