To promote cooperation between centralized energy storage and multiple wind farms for the sustainable development of shared energy storage, this paper explores the resource allocation and trading mechanisms for centralized shared energy storage in multi-wind farms. First, a joint operational framework for multiple wind farm shared energy storage is constructed to achieve smooth and stable grid connection of wind farms and shared use of centralized independent energy storage. Based on the Vickrey-Clarke-Groves (VCG) mechanism, a two-stage incentive-compatible trading mechanism for energy storage sharing is proposed. In the first stage, a master-slave game model with multiple wind farms as leaders and shared energy storage as followers determines the initial transaction prices between the wind farm cluster and the energy storage for each time period. The second stage uses a two-way auction mechanism to refine the initial transaction price, aiming to maximize social welfare. Additionally, the final transaction price is formed by using the compensation method for the difference between revenues and expenditures to address the imbalance between revenues and expenditures of the VCG mechanism. Finally, the effectiveness of the proposed mechanism is verified by an example using wind power data from the Xinjiang region. Compared with the trading results of wind farms and shared energy storage under the fixed-price trading model, the revenues of the wind farms are increased by 11.14%, 5.26% and 6.61%, respectively. The mechanism provides a reference for promoting the development of centralized shared energy storage.