Air traffic control increasingly depends on information and communication technology (ICT) to manage traffic flow through highly congested and increasingly interdependent airspace regions. While these systems are critical to ensuring the efficiency and safety of our airspace, they are also increasingly vulnerable to cyber threats that could potentially lead to reduction in capacity and/or reorganization of traffic flows. In this paper, we model various cyber threats to air traffic control systems, and analyze how these attacks could impact the flow of aircraft through the airspace. To perform this analysis, we consider a model for wide-area air traffic based on a dynamic queuing network model. Then we introduce three different attacks (Route Denial of Service, Route Selection Tampering, and Sector Denial of Service) to the air traffic control system, and explore how these attacks manipulate the sector flows by evaluating the queue backlogs for each sector's outflows. Furthermore, we then explore graph-level vulnerability metrics to identify the sectors that are most vulnerable to various flow manipulations, and compare them to case-study simulations of the various attacks. The results suggest that Route Denial of Service attacks have a significant impact on the target sector and lead to the largest degradation to the overall air traffic flows. Furthermore, the impact of Sector Denial of Service attack impacts are primarily confined to the target sector, while the Route Selection Tampering impacts are mostly confined to certain aircraft.