This paper presents a novel probabilistic distributed framework based on movement primitives for flexible robot assembly. Since the modern advanced industrial cell usually deals with various scenarios that are not fixed via-point trajectories but highly reconfigurable tasks, the industrial robots used in these applications must be capable of adapting and learning new in-demand skills without programming experts. Therefore, we propose a probabilistic framework that could accommodate various learning abilities trained with different movement-primitive datasets, separately. Derived from the Bayesian Committee Machine, this framework could infer new adapting trajectories with weighted contributions of each training dataset. To verify the feasibility of our proposed imitation learning framework, the simulation comparison with the state-of-the-art movement learning framework task-parametrised GMM is conducted. Several key aspects, such as generalisation capability, learning accuracy and computation expense, are discussed and compared. Moreover, two real-world experiments, i.e. riveting picking and nutplate picking, are further tested with the YuMi collaborative robot to verify the application feasibility in industrial assembly manufacturing.