Recommender system can provide users with the required information accurately and efficiently, playing a very important role in improving users' life experience. Although knowledge graph-based recommender system can solve the sparsity and cold start problems faced by traditional recommender system, it cannot handle the cross-domain cold start problem and cannot provide multi-domain recommendations. Therefore, this paper focuses on multi-domain item-item (I2I) recommendation based on cross-domain knowledge graph embedding by analyzing the association between items of the same domain and the interaction between items of diverse domains with the aid of knowledge graph that contains rich information. Firstly, a cross-domain knowledge graph chiasmal embedding approach is proposed to efficiently interact all items in multiple domains. To help achieve both homo-domain embedding and hetero-domain embedding of items, a binding rule is put forward. Secondly, a multi-domain I2I recommendation method is presented to efficiently recommend items in multiple domains, which is a recommendation method based on link prediction of knowledge graph. Finally, the proposed methods are compared and analyzed with some benchmark methods using two datasets. The experimental results show that the proposed methods achieve better link prediction results and multi-domain recommendation results.