Measurement of the chemical composition of gases sampled through a small hole in the substrate can be a useful diagnostic for investigations of the chemistry of chemical vapor deposition (CVD) processes. Ideally, one would measure the composition of the gas at the growth surface. However, the flow disturbance due to sampling causes the conditions at the mouth of the orifice to be different from those at the growth surface. Unless the orifice diameter is sufficiently small, relative to the thickness of chemical and thermal boundary layers above the growth surface, the sampled composition will differ from the composition at the growth surface. In this work, we present results of two-dimensional simulations of the flow, heat transfer, and chemical reactions in an axisymmetric stagnation point flow with gas sampling through a small orifice in the substrate on the symmetry axis of the flow field. Detailed results are given for atmospheric-pressure radio-frequency plasma CVD of diamond, corresponding to experiments performed in our laboratory. We also present more general results, approximate analytical representations of the flow field, and scaling rules for the size of the disturbance due to the sampling orifice.