To understand the correlation and the radiation mechanism of flare emission in different wavelength bands, we have coordinated a number of telescopes to observe Sgr A* simultaneously. We focus only one aspect of the preliminary results of our multi-wavelength observing campaigns, namely, the short time scale variability of emission from Sgr A* in near-IR, X-ray and radio wavelengths. The structure function analysis indicate most of the power spectral density is detected on hourly time scales in all wavelength bands. We also report minute time scale variability at 7 and 13mm placing a strong constraint on the nature of the variable emission. The hourly time scale variability can be explained in the context of a model in which the peak frequency of emission shifts toward lower frequencies as a self-absorbed synchrotron source expands adiabatically near the acceleration site. The short time scale variability, on the other hand, places a strong constraint on the size of the emitting region. Assuming that rapid minute time scale fluctuations of the emission is optically thick in radio wavelength, light travel arguments requires relativistic particle energy, thus suggesting the presence of outflow from Sgr A*.