The successful utilization of premixed oxygen/acetylene flames in the chemical vapor deposition of diamond has led to an interest in scaleable configurations, realized in this work using a stagnation-flow reactor. Through a computational model that incorporates detailed gas-phase kinetics, molecular transport, and surface chemistry, the roles of process variables such as flame stoichiometry, rate of strain, and the use of flow diluents are explored. For parameterization, we have characterized diamond deposition using the surface fluxes of atomic hydrogen and methyl radical, and have correlated the modeling results with experimental data from a scaled-up stagnation-flow reactor. Flame temperature, stoichiometry, and diluent addition were found to have a strong effect on diamond deposition, enabling optimization of the diamond deposition rates with a constraint on diamond film quality. Modeling results are presented, and the utility of the flame model in conjuction with an experimental diamond deposition study is demonstrated.