Highly accurate reaction rate constants may be extracted from data obtained in well-developed (laminar or turbulent) diffusive flow over a wide range of experimental conditions. In many cases, data obtained in the core of such a flow may be treated as if the flow were one dimensional, leaving only a small correction for radial diffusion. This correction factor is derived analytically and presented in terms of easily observed quantities. The correction is robust; experimental and theoretical evidence is presented showing that it is insensitive to assumed axial symmetry and remains small so long as the interaction between the core and wall of a flowtube falls within well-defined bounds. The major limitations to accuracy in our high-pressure flow kinetics system (HPFS) are discussed in conjunction with observations of bimolecular reaction rate constants made over a very wide range of experimental conditions for the reactions OH + ethane --> products and OH + cyclohexane --> products. In the current experiment, accuracy for hydroxyl radical reactions is limited to roughly 12% for pressures of nitrogen ranging from 2 to 600 Torr. The accuracy in the measured ratio of two hydroxyl radical reaction rate constants is roughly 6%. Accuracy is currently limited primarily by absolute velocity measurements and by radical detection sensitivity. Strategies for further improving the accuracy of the high-pressure flow (HPF) technique are discussed.