The source of emission from Sgr A*, the supermassive black hole at the Galactic Center, is still unknown. Flares and data from multiwavelength campaigns provide important clues about the nature of Sgr A* itself. Here we attempt to constrain the physical origin of the broadband emission and the radio flares from Sgr A*. We developed a time-dependent jet model, which for the first time allows one to compare the model predictions with flare data from Sgr A*. Taking into account relevant cooling mechanisms, we calculate the frequency-dependent time lags and photosphere size expected in the jet model. The predicted lags and sizes are then compared with recent observations. Both the observed time lags and size-frequency relationships are reproduced well by the model. The combined timing and structural information strongly constrain the speed of the outflow to be mildly relativistic, and the radio flares are likely to be caused by a transient increase in the matter channelled into the jets. The model also predicts light curves and structural information at other wavelengths which could be tested by observations in the near future. We show that a time-dependent relativistic jet model can successfully reproduce: (1) the quiescent broadband spectral energy distribution of Sgr A*, (2) the observed 22 and 43 GHz light curve morphologies and time lags, and (3) the frequency-size relationship. The results suggest that the observed emission at radio frequencies from Sgr A* is most easily explained by a stratified, optically thick, mildly relativistic jet outflow. Frequency-dependent measurements of time-lags and intrinsic source size provide strong constraints on the bulk motion of the jet plasma.