This paper proposes a distributed model predictive control (DMPC) algorithm for the formation flight of a group of UAVs modeled by six degree-of-freedom (6-DoF) spatial kinematics. The formation system has a leader-follower structure with the leader cruising at a constant linear velocity during the flight, and the UAVs transmit data in a unidirectional order. The DMPC algorithm utilizes the unidirectional structure through the reception and transmission of an assumed output sequence as the reference trajectory, which is constructed from the solutions to the local DMPC problem and the prediction model. Based on the interactions between UAVs, convergence and stability of the multi-UAV formation are ensured by the terminal constraints and recursive feasibility of the DMPC optimization. Simulations involving time-delays, packet drops and turbulence effect are conducted to verify the effectiveness of the proposed algorithm. Comparisons with non-unidirectional data transmissions further demonstrate that the unidirectional structure plays a critical role in the convergence performance.