Oil droplets in aqueous surfactant solution show spontaneous self-propulsion and dynamics ranging from straight-line to unsteady motion with increasing Péclet number. Recent studies have shown that products of interfacial activity (oil-filled micelles) can lead to multistable higher-mode flow fields and chemorepulsive phenomena. To investigate such chemodynamic effects, we have studied disk-like flattened droplets that are pinned at the top and bottom of the reservoir and produce only pumping flow. With increasing droplet radius we observe the following: (i) vortical structures generated by the droplet migrating around the interface, (ii) bistability between a dipolar and quadrupolar flow mode, and, eventually, (iii) a transition to multipolar modes. For a deeper analysis, we measured flow fields by particle image velocimetry and compared them to a hydrodynamic model based on a Brinkman squirmer. A simultaneous quantification of the flow fields and oil-filled micelle distribution suggests that a local buildup of chemical products leads to a saturation of the surface, which affects the propulsion mechanism. Hence, we describe the interfacial activity dynamics in time and space.