We demonstrate that polarimetric interferometry can be used to extract precise spatial information about compact polarized flares of Sgr A*. We show that, for a faint dynamical component, a single interferometric baseline suffices to determine both its polarization and projected displacement from the quiescent intensity centroid. A second baseline enables two-dimensional reconstruction of the displacement, and additional baselines can self-calibrate using the flare, enhancing synthesis imaging of the quiescent emission. We apply this technique to simulated 1.3 mm wavelength observations of a "hot spot" embedded in a radiatively inefficient accretion disk around Sgr A*. Our results indicate that, even with current sensitivities, polarimetric interferometry with the Event Horizon Telescope can achieve ~5 μas relative astrometry of compact flaring structures near Sgr A* on timescales of minutes.
