High-velocity outflows from supermassive black holes have been invoked to explain the recent identification of strong absorption features in the hard X-ray spectra of several quasars. Here, Monte Carlo radiative transfer calculations are performed to synthesize X-ray spectra from models of such flows. It is found that simple, parametric biconical outflow models with plausible choices for the wind parameters predict spectra that are in good qualitative agreement with observations in the 2-10 keV band. The influence on the spectrum of both the mass-loss rate and opening angle of the flow are considered: the latter is important since photon leakage plays a significant role in establishing an ionization gradient within the flow, a useful discriminant between spherical and conical outflow for this and other applications. Particular attention is given to the bright quasar PG 1211+143 for which constraints on the outflow geometry and mass-loss rate are discussed subject to the limitations of the currently available observational data.