This paper provides a complete framework to illustrate the pioneering application of drones in traffic safety analysis, which includes the design of drone operations, extraction of vehicle trajectories using state-of-the-art computer vision techniques, derivation of vehicle kinematic profiles, and a comprehensive traffic safety analysis. We utilize well-known Surrogate Safety Measures (SSM) like the Time-To-Collision (TTC) and the Post-Encroachment-Time (PET) to detect risky interactions and observe their spatial distribution using high-quality, detailed trajectory data in an urban environment. This framework is exemplified with a case study of two busy signalized intersections in the center of Manchester, UK, where a traffic data collection campaign with a swarm of drones was organized. One of the intersections includes an elevated freeway as well. The analysis includes a comprehensive traffic safety assessment, identifying areas within the intersections prone to crashes. Furthermore, we delve into the root causes of these risky interactions through the identification of conflicting critical movements. Finally, we use the data to establish an empirical relationship between traffic variables like speed with the frequency of near-crash events.