A new light scattering method is developed to measure scattering amplitude fluctuations resulting from either internal motions of flexible macromolecules or rotations of rigid particles. With a single-beam two-color cross-correlation scheme, the technique becomes insensitive to rapid phase fluctuations of the scattered light produced by translational motions of the scattering particles. We frame the scattering theory so as to encompass rotations and number fluctuations of small particles in a steady laminar flow. Experiment verifies the theory and demonstrates its applications. The technique can be used to measure the magnitudes of the local velocity and the flow vorticity. It can also be used to measure internal motions and shape fluctuations of flexible macromolecules. The advantages of the technique are its high spatial resolution, fast temporal response, and ease of use.