A new analysis of the connection between black hole mass and radio luminosity in radio-selected flat-spectrum quasars (FSQs) is presented. In contrast to recent claims in the literature, we find no evidence that the black hole masses of radio-selected FSQs are systematically lower than those of luminous optically selected radio-loud quasars. The black hole masses of the FSQs are estimated via the virial black hole mass estimator which utilizes the linewidth of the Hβ emission line as a tracer of the central gravitational potential. By correcting for the inevitable effects of inclination, incurred as a result of the FSQs being viewed close to the line of sight, we find that the black hole masses of the FSQs with intrinsically powerful radio jets are confined, virtually exclusively, to Mbh > 108 Msolar. This is in good agreement with previous studies of optically selected FSQs and steep-spectrum radio-loud quasars. Finally, following the application of a realistic Doppler boosting correction, we find that the FSQs occupy a wide range in intrinsic radio luminosity, and that many sources would be more accurately classified as radio-intermediate or radio-quiet quasars. This range in radio luminosity suggests that the FSQs are fully consistent with an upper boundary on radio power of the form L5GHz~Mbh2.5.