Domino effects are a complex phenomenon of accident escalation with high uncertainty, which could lead to catastrophic consequences. Predicting the probability of domino effects presents a great challenge in the field of process safety. In multi-level domino chains, synergistic effects of accidents would further raise the complexity of probability prediction since escalation vectors emitted from those accidents may be coupled. In this paper, four categories of synergistic effects are classified according to the type of accidents and their place on the domino accident sequence. Subsequently, specific models for estimating escalation probability under different synergistic accident scenarios are proposed based on the widely-used probit models, allowing the analysis of the coupling effects of escalation vectors. A probability prediction method for domino chains is further developed using Bayesian Network. The application of the developed method is demonstrated by a case study, and the domino probability is estimated accounting for the synergistic effects and all possible accident scenarios. The key units for promoting accident propagation are further identified through posterior probability analysis. The method would be helpful for domino risk assessment and management of any chemical industrial area.