Magnetic microparticles, assembled into chains that are actuated with rotating magnetic fields, can be used as microstirrers to promote fluid transport and biochemical reactions in microfluidic systems. We show that, within a certain range of magnetic field rotation frequency, the microstirrers exhibit a coherent collective motion: the rotating magnetic particle chains move throughout the volume of a flat fluid cell and generate very strong (~1 mm/s) and global (9 mm) vortical fluid flows, with many eddy-type substructures that fluctuate continuously in time, resembling turbulent flow. The collective motion makes the microstirrers not only defy gravity, but also to move against magnetic field gradients. The induced fluid flow is directly related to the stirring rate and the amount of magnetic particle chains. The observed behavior is caused by the magnetic and hydrodynamic interactions between the magnetic microparticles and the fluid. We utilized the phenomenon of swarming particles to enhance biochemical assays with magnetic capture particles (4000/µL) and IgG targets (500 pM). When compared to a reference system of sedimented magnetic capture particles, magnetic actuation leads to both a ~9 times increase in the initial assay kinetics as well as a ~7 times increase of target capture signal after 30 minutes.