The article introduces a novel approach to foster collaborative aerial 3D printing by leveraging the dexterous flexibility of multiple UAVs working in tandem towards autonomous construction. This cooperative operation effectively overcomes payload limitations through synchronized deployment. Nevertheless, the transformation of UAVs into aerial construction agents poses a pivotal challenge, demanding efficient coordination of task planning and effective execution among multiple collaboratively working UAVs. In pursuit of addressing this challenge, the proposed innovative framework introduces a novel chunk-decomposition strategy supported by a reactive task assignment mechanism, dynamically allocating additive manufacturing tasks based on a dependency graph derived from decomposed chunks. Furthermore, the framework promotes parallelization by minimizing interdependencies thereby reducing the overall makespan. It also incorporates conflict resolution among UAVs during the assignment process by employing probabilistic fitness scores and penalizing the probability of conflicts. Conflicts that emerge during printing execution are addressed in a decentralized manner through trajectory sharing among UAVs. This entails dynamically determining one UAV suspending its movement until conflicts are resolved. The proposed framework's effectiveness is evaluated through a GAZEBO-based simulation setup, showcasing its potential in deploying multiple UAVs for the simultaneous printing of large-scale 3D structures. - Video overview: https://youtu.be/bLnzcLrD1NA