The flow-driven transport of interacting micron-sized particles occurs in many soft matter systems spanning from the translocation of proteins to moving emulsions in microfluidic devices. Here we combine experiments and theory to investigate the collective transport properties of colloidal particles along a rotating ring of optical traps. In the corotating reference frame, the particles are driven by a vortex flow of the surrounding fluid. When increasing the depth of the optical potential, we observe a jamming behavior that manifests itself in a strong reduction of the current with increasing particle density. We show that this jamming is caused by hydrodynamic interactions that enhance the energetic barriers between the optical traps. This leads to a transition from an over- to an under-critical tilting of the potential in the corotating frame. Based on analytical considerations, the enhancement effect is estimated to increase with increasing particle size or decreasing radius of the ring of traps. Measurements for different ring radii and Stokesian dynamics simulations for corresponding particle sizes confirm this. The enhancement of potential barriers in the flow-driven system is contrasted to the reduction of barriers in a force-driven one. This diverse behavior demonstrates that hydrodynamic interactions can have a very different impact on the collective dynamics of many-body systems. Applications to soft matter and biological systems require careful consideration of the driving mechanism and of the role of hydrodynamic interactions.