Advanced Air Mobility (AAM) envisions multiple classes of uncrewed aircraft systems (UAS) performing a wide variety of tasks ranging from package delivery to infrastructure inspections. The scale and complexity of future AAM operations require new frameworks for UAS traffic management (UTM), with autonomous and federated air traffic management (ATM) services governing different regions of the AAM airspace. Current UTM solutions are often centralized, and assume that one entity optimizes UAS trajectories and schedules. However, current AAM concepts-of-operations depict competing UAS service suppliers (USS) in charge of ATM services for their own airspace region. We propose a distributed optimization-based approach to UTM, wherein each individual region solves a local traffic flow management problem, and communicates with other regions when necessary. To do so, we design a heuristic that enables distributed UAS traffic flow management, requiring no centralized coordination. We implement this heuristic and test it on a synthetic set of UAS trajectories, operating in an airspace divided into multiple regions. We show that, at a cost of increased delays relative to the centralized solution, our heuristic obtains a feasible solution, even though no singular region has access to trajectory information of other regions.