This paper presents a control strategy for multiple vehicles that cooperatively transport a flexible payload. To this end, an algorithm is developed which generates optimal trajectories for the vehicles to follow. Solving an optimization problem composes the core of the algorithm. The problem is first decomposed over the vehicles using the Alternating Direction Method of Multipliers (ADMM) algorithm. This results in each vehicle solving a sub-problem to generate its own optimal trajectory. The algorithm instructs that the optimization problem be solved repeatedly in a receding horizon fashion, making it fit into a distributed model predictive control (DMPC) framework. One ADMM iteration is performed per DMPC iteration, reducing the inter-agent communication rate. Numerical validation of the developed control scheme is performed and the results are presented.