The formation of polycyclic aromatic hydrocarbon (PAH) molecules in carbon-rich stellar outflows is modeled with a detailed chemical kinetic scheme applied to stellar envelope profiles of gas density and temperature. These envelope models include the average effects of strong periodic shocks at the inner envelope boundary and radiation pressure acceleration of the stellar outflow. The chemical kinetic scheme is based on the work of Frenklach & Feigelson with revisions and extentions from recent combustion literature on soot formation. The model explicitly includes organic molecules, free radicals, and aromatics up to the size of cyclopenta[cd]pyrene (C18H12). Chemical concentration profiles were calculated for several envelope models by integrating the coupled continuity equations that include spherically expanding flows from an inner boundary at the shock formation radius, where the chemical composition is assumed to be at thermal equilibrium. The influence of the "inverse greenhouse" effect experienced by small PAHs has been investigated and shown to increase the PAH yield by many orders of magnitudes. A detailed examination of the various chemical kinetic routes towards closure of the first aromatic ring, the bottleneck in any soot formation scheme, shows that the route through propargyl radicals (C3H3) could be an important channel to produce benzene. It is pointed out that the combustion community has not reached a consensus regarding chemical kinetic schemes for soot formation, and thus future work on PAH formation in stellar envelopes may require further revisions to the kinetic scheme. The PAH formation yields are found to be extremely sensitive to gas density and temperature, and they are much smaller than values inferred from the observed dust content of late-type carbon-rich stellar envelopes. Assuming the chemical kinetic scheme is substantially correct, it is therefore unlikely that aromatic molecules are generated in the stellar outflow itself. Instead, PAH formation might be initiated very close to the photosphere. One possible mechanism is that PAHs may form and accumulate in gas parcels subjected to oscillatory quasi-ballistic trajectories induced by shocks close to the photosphere.