A flow rate sensing system can include an optical waveguide, an optical interrogator that detects optical scatter in the optical waveguide, and an emitter that produces vibration in response to flow, the optical scatter being influenced by the vibration. A method of measuring flow rate can include detecting optical scattering in an optical waveguide, the optical scattering varying in response to changes in vibration produced by an emitter, and the vibration changing in response to the flow rate changing. A well system can include at least one tubular string positioned in a wellbore, multiple locations at which fluid flows between an interior and an exterior of the tubular string, multiple emitters, each of which produces vibration in response to the flow between the interior and the exterior of the tubular string, and an optical waveguide in which optical scatter varies in response to changes in the vibration.