Fluid flows generated by motile cilia are guiding the establishment of the left-right asymmetry of the body in the vertebrate left-right organizer. Competing hypotheses have been proposed: the direction of flow is sensed either through mechanosensation, or via the detection of chemical signals transported in the flow. We investigated the physical limits of flow detection to clarify which mechanisms could be reliably used for symmetry breaking. We integrated parameters describing cilia distribution and orientation obtained in vivo in zebrafish into a multiscale physical study of flow generation and detection. Our results show that the number of immotile cilia is too small to ensure robust left and right determination by mechanosensing, given the large spatial variability of the flow. However, motile cilia could sense their own motion by a yet unknown mechanism. Finally, transport of chemical signals by the flow can provide a simple and reliable mechanism of asymmetry establishment.