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We use the Very Long Baseline Array to conduct high precision astrometry of a sample of 33 compact, flat spectrum, variable radio sources in the direction of the Galactic plane (Becker et al. 2010). Although Becker et al. (2010) ruled out a few potential scenarios for the origin of the radio emission, the study could not rule out that these sources were black hole X-ray binaries (BHXBs). Most known BHXBs are first detected by X-ray or optical emission when they go into an outburst, leaving the larger quiescent BHXB population undiscovered. In this paper, we attempt to identify any Galactic sources amongst the Becker et al. (2010) sample by measuring their proper motions as a first step to finding quiescent BHXB candidates. Amongst the 33 targets, we could measure the proper motion of six sources. We find that G32.7193$-$0.6477 is a Galactic source and are able to constrain the parallax of this source with a 3$σ$ significance. We found three strong Galactic candidates, G32.5898$-$0.4468, G29.1075$-$0.1546, and G31.1494$-$0.1727, based purely on their proper motions, and suggest that G29.1075$-$0.1546, is also likely Galactic. We detected two resolved targets for multiple epochs (G30.1038+0.3984 and G29.7161$-$0.3178). We find six targets are only detected in one epoch and have an extended structure. We cross-match our VLBA detections with the currently available optical, infrared and X-ray surveys, and did not find any potential matches. We did not detect 19 targets in any VLBA epochs and suggest that this could be due to limited $uv$-coverage, drastic radio variability or faint, extended nature of the sources.