The black hole at the Galactic Center, Sgr A*, is the prototype of a galactic nucleus at a very low level of activity. Its radio through submm-wave emission is known to come from a region close to the event horizon, however, the source of the emission is still under debate. A successful theory explaining the emission is based on a relativistic jet model scaled down from powerful quasars. We want to test the predictive power of this established jet model against newly available measurements of wavelength-dependent time lags and the size-wavelength structure in Sgr A*. Using all available closure amplitude VLBI data from different groups, we again derived the intrinsic wavelength-dependent size of Sgr A*. This allowed us to calculate the expected frequency-dependent time lags of radio flares, assuming a range of in- and outflow velocities. Moreover, we calculated the time lags expected in the previously published pressure-driven jet model. The predicted lags are then compared to radio monitoring observations at 22, 43, and 350 GHz. The combination of time lags and size measurementsfg imply a mildly relativistic outflow with bulk outflow speeds of gamma beta 0.5-2. The newly measured time lags are reproduced well by the jet model without any major fine tuning. The results further strengthen the case for the cm-to-mm wave radio emission in Sgr A* as coming from a mildly relativistic jet-like outflow. The combination of radio time lag and VLBI closure amplitude measurements is a powerful new tool for assessing the flow speed and direction in Sgr A*. Future VLBI and time lag measurements over a range of wavelengths will reveal more information about Sgr A*, such as the existence of a jet nozzle, and measure the detailed velocity structure of a relativistic jet near its launching point for the first time.