The limits to the cosmic microwave background radiation (CBR) temperature anisotropy derived from the results of the University of Califronia at Santa Barbara South Pole degree-scale experiment are translated into upper bounds on large-scale deviations from the Hubble flow. Calculations involve the Einstein-de Sitter, dark matter-dominated cosmology with standard thermal history (no early reheating) and gravitationally formed large-scale structure, seeded by random, Gaussian-distributed, adiabatic inhomogeneities. The results are independent of the Hubble constant, the composition of dark matter, and the power spectrum of primordial perturbations. The lack of measurable CBR anisotropy in this experiment implies very low upper bounds upon the rms amplitude V(R) of the streaming motion within a Gaussian window of radius R: V(max)(R > 4000 km s-1) < 200 km s-1, and V(max)(R > 7500 km s-1) < 100 km s-1. Thus, the smoothness of the CBR at theta approximately 1-degrees-2-degrees and the apparent large-amplitude (approximately 500 km s-1) deviations from pure Hubble flow at R greater than or similar to 4000 km s-1 cannot be simultaneously explained in the framework of usual large-scale structure formation models based on the assumptions involved in this calculation.