A superfine time structure has been detected recently via hard X-ray satellite observations during solar flares. Some pulses are hundreds of milliseconds in length. Time series are sharply nonstationary sequences of overlapping pulses. We interpreted a similar time structure in a model of the nonstationary kinetics of accelerated electron beams. In this work, we present calculation results of the degree of polarization of the hard X rays of solar flares with millisecond pulses. The dependence of the polarization degree on the plasma concentration, radiation energy, and the observation angle has been derived from calculations with the thick-target nonstationary kinetics model for rectangular and triangular individual pulses of accelerated electrons in the region of injection with the angular dependence cos2nθ. It is shown that the degree of polarization does not exceed 78% and decreases down to 50–65% 20 s after the beginning of the injection.