The statistical model of scattered by flowing Brownian particles coherent radiation is suggested. The model includes the random Doppler shifts caused by particle Brownian motion and the speckle fluctuations caused primarily by the flow motion of particles. Analytical expressions are obtained for the correlation function, power spectrum, and spectral width of scattered radiation in the imaging geometry typically used in optical coherence tomography (OCT). It is shown that the spectral density has the Voigt shape, a well-known spectral profile from atomic and molecular spectroscopy. The approach enables the choice of the experimental regimes for the measurement of Brownian particle motion parameters even in the presence of flow. These regimes are characterized by the dominant contribution of Brownian motion in the spectral width of the flow-caused Doppler shift component. Further, the new formalism suggests that prior attempts to extract transverse flow velocity are only valid at near-perpendicular geometry. The impact of the small scattering volume contributing to the OCT signal is also discussed.