A Brillouin dynamic grating (BDG) can be used for distributed birefringence measurement in optical fibers, offering high sensitivity and spatial resolution for sensing applications. However, it is quite a challenge to simultaneously achieve dynamic measurements with both high accuracy and high spatial resolution. In this work, we propose a sensing mechanism to achieve distributed phase-matching measurement using a chirped pulse as a probe signal. In BDG reflection, the peak reflection corresponds to the highest four-wave mixing (FWM) conversion efficiency, and it requires the Brillouin frequency in the fast and slow axes to be equal, which is called the phase-matching condition. This condition changes at different fiber positions, which requires a range of frequency injection for the probe wave. The proposed method uses a chirped pulse as a probe wave to cover this frequency range associated with distributed birefringence inhomogeneity. This allows us to detect distributed phase matching for birefringence changes that are introduced by temperature and strain variations. Thanks to the single shot and direct time delay measurement capability, the acquisition rate in our system is only limited by the fiber length. Notably, unlike conventional BDG spectrum recovery-based systems, the spatial resolution here is determined by both the frequency chirping rate of the probe pulse and the birefringence profile of the fiber. In the experiments, an acquisition rate of 1 kHz (up to fiber length limits) and a spatial resolution of 10 cm using a 20 ns probe pulse width are achieved. The minimum detectable temperature and strain variation are 5.6 mK and 0.37 με along a 2 km long polarization-maintaining fiber (PMF).