Existing approaches for robotic control of magnetic swarms are not capable of generating magnetic aggregates precisely in an arbitrarily specified target region in a fluidic flow environment. Such a swarm control capability is demanded by medical applications such as clinical embolization (i.e., localized clogging of blood vessels). This paper presents a new magnetic swarm control strategy to generate aggregates only in a specified target region under fluidic flow. Within the target region, the magnetic field generates sufficiently large magnetic forces among magnetic particles to maintain the aggregates' integrity at the junctions of blood vessels. In contrast, unintended aggregates outside the target region are disassembled by fluidic shear. The aggregation control approach achieved a mean absolute error of 0.15 mm in positioning a target region and a mean absolute error of 0.30 mm in controlling the target region's radius. With thrombin coating, 1 μm magnetic particles were controlled to perform embolization both in vitro (using microfluidic channel networks) and ex vivo (using porcine tissue). Experiments proved the effectiveness of the swarm control technique for on-demand, targeted embolization.