We present theory and a simulation framework to model three-body collisions and gas phase recombination in dilute atom/diatom mixtures of pure oxygen (O/O2) and nitrogen (N/N2) using the Quasi-Classical Trajectory method. We formulate a three-body collision rate constant based on the lifetimes of binary collisions and initialize three-body collisions by sampling the arrival time of a third body within the lifetimes of pre-simulated binary collisions. We use this method to calculate distributions of recombined product energies, probabilities of recombination, and recombination rate constants through different collision pathways. Long-lived binary atom-diatom collisions are observed, but are too rare to play a dominant role in the recombination process for shock-heated air near the equilibrium conditions studied. The resulting recombination rate constants are within an order of magnitude of the predictions of detailed balance. Notably, the recombination simulation framework does not appeal to the principle of detailed balance and could be useful for studying conditions far from equilibrium.