The growing interest in studying social behaviours of swarming fruit flies, Drosophila melanogaster, has heightened the need for developing tools that provide quantitative motion data. To achieve such a goal, multi-camera three-dimensional tracking technology is the key experimental gateway. We have developed a novel tracking system for tracking hundreds of fruit flies flying in a confined cubic flight arena. In addition to the proposed tracking algorithm, this work offers additional contributions in three aspects: body detection, orientation estimation, and data validation. To demonstrate the opportunities that the proposed system offers for generating high-throughput quantitative motion data, we conducted experiments on five experimental configurations. We also performed quantitative analysis on the kinematics and the spatial structure and the motion patterns of fruit fly swarms. We found that there exists an asymptotic distance between fruit flies in swarms as the population density increases. Further, we discovered the evidence for repulsive response when the distance between fruit flies approached the asymptotic distance. Overall, the proposed tracking system presents a powerful method for studying flight behaviours of fruit flies in a three-dimensional environment.