Safe and scalable dynamic autonomous data interaction between medical institutions can increase the number of clinical trial records, which is of great significance for improving the level of medical trial collaboration, especially for clinical decision-making with regard to rare diseases. Through a preset authorization access and consensus mechanism, consortium chain provides integrity and traceability management for medical clinical data. However, how to enable users have ownership of their own medical data and share their medical data safely and dynamically between different medical institutions remains an area of particular concern. To achieve dynamic communication between medical consortium chains, this paper proposes (i) a cross-chain communication mechanism by simplifying the heterogeneous node communication topology and (ii) the construction rules of the node identity credibility path-proof to carry out dynamic construction and verification of the path-proof for cross-chain transactions. In addition, the consensus of the cross-chain transaction is modeled as a threshold digital signature process with multiple privileged subgroups; thus, the intra-chain consortium consensus based on the verification node list is extended to the cross-chain consensus. A smart contract deployment and execution scheme based on rational node value transfer mechanism is proposed by analyzing the value transfer game between nodes. Experimental results showed that the proposed scheme can not only enable patients to share their records safely and autonomously in an authorized medical consortium chain within milliseconds but also realize dynamic adaptive interaction among heterogeneous consortium chains.