The design, performance, and calibration of the seven flow proportional counters (FPCs) used during AXAF ground calibration are described. Five of the FPCs served as beam normalization detectors (BNDs), and two were used in the telescope focal plane in combination with a set of apertures to measure the point response functions and effective areas of the AXAF mirrors and transmission gratings. The BNDs also provide standards for determining the effective areas of the several telescope/grating/flight-detector combinations. With useful energy resolution and quantum efficiency over the entire 100-eV to 10 keV AXAF energy band, the FPCs provided most of the data acquired during AXAF calibration. Although the principles of proportional counter operation are relatively simple, AXAF's stringent calibration goals require detailed calibration and modeling of such effects as window- support-wire obscuration, window deformation between the support wires, electron diffusion and avalanche processes, gain nonuniformities, and gas pressure and temperature variations. Detector aperture areas and signal processing deadtime must also be precisely determined, and detector degradation during the many months of AXAF calibration must be prevented. The FPC calibration program is based on measurement of individual components (such as window transmission and aperture size) and the relative quantum efficiencies of complete detector systems, as well as absolute QE calibration of selected detectors at the BESSY synchrotron, an x-ray source of precisely known intensity.