Multiple robot systems are favored for object manipulation and transportation, especially for large objects. However, in more complex manipulation such as flipping, these systems encounter a new challenge, configuration disconnectivity of manipulators. Grasping objects by manipulators will impose closed-chain constraints on the system, which in turn limits the feasible motions of manipulators and further compromises the configuration connectivity. Multiple mobile manipulator systems show much more flexibility in object manipulation with the mobility of the mobile platform and have the potential to address the above problem. In this paper, a novel planning framework is proposed for complex flipping manipulation by incorporating platform motions and regrasping. Firstly, two types of trajectories, mobile manipulator planning and regrasping planning, are classified and can be assigned different priorities for different tasks. Secondly, corresponding planning methods are designed for each type of trajectory. Specifically, in mobile manipulator planning, the configuration of the platform is determined through optimization to ensure connectivity when the manipulator approaches configuration boundaries. In regrasping planning, closed-chain constraints are temporarily disregarded and the manipulation capabilities are prioritized to facilitate subsequent planning. Finally, the structure of the overall planning framework is provided. Experimental results demonstrate that the proposed planner efficiently plans the motions of the system to accomplish flipping manipulation. Additionally, a comprehensive experiment emphasizes the significance of our planner in extending the capabilities of multiple mobile manipulator systems in complex tasks.