Sgr A*, the massive black hole at the center of the Galaxy, varies in radio through X-ray emission on hourly timescales. The flare activity is thought to arise from the innermost region of an accretion flow onto Sgr A*. We present simultaneous light curves of Sgr A* in radio, submillimeter and X-rays that show a possible time delay of 110 ± 17 minutes between X-ray and 850 μm suggesting that the submillimeter flare emission is optically thick. At radio wavelengths, we detect time lags of 20.4 ± 6.8, 30 ± 12, and 20 ± 6 minutes between the flare peaks observed at 13 and 7 mm (22 and 43 GHz) in three different epochs using the VLA. Linear polarization of 1% ± 0.2% and 0.7 ± 0.1% is detected at 7 and 13 mm, respectively, when averaged over the entire observation on 2006 July 17. A simple model of a bubble of synchrotron-emitting electrons cooling via adiabatic expansion can explain the time delay between various wavelengths, the asymmetric shape of the light curves, and the observed polarization of the flare emission at 43 and 22 GHz. The derived physical quantities that characterize the emission give an expansion speed of vexp ~ 0.003–0.1 c, magnetic field of B ~ 10–70 G, and particle spectral index p ~ 1–2. These parameters suggest that the associated plasma cannot escape from Sgr A* unless it has a large bulk motion.