Ultra reliable and low latency communications (uRLLC) is one of the most significant requirements for future wireless networks. The conventional terrestrial base stations cannot always provide the required uRLLC for emerging applications and scenarios, e.g., Tactile Internet services or when a large number of users get connected during an event. Therefore, multilayer airborne networks with low/medium/high altitude platforms can be deployed as an effective solution to offer capacity and coverage along with required latency and reliability for wireless networks. In this article, we propose a three layers airborne network to support the uRLLC requirement in wireless networks. Optimized link selection schemes have been provided based on Polychromatic Sets (PSets) theory to focus on the uRLLC. With the optimized link selection algorithm, multiple properties of the airborne platforms are exploited and the links are selected based on the multi-constrained requirements to support the desired performance of the airborne network. Moreover, two links distribution schemes have been proposed as distributed greedy scheme and centralized greedy scheme to demonstrate the deployment of proposed airborne network. Numerical results show that both PSets-based links distribution schemes outperform the general distribution schemes on average latency and overall reliability also known as unassociated ratio, which strongly supports the uRLLC in considered airborne networks.