Healthcare innovations are increasingly becoming reliant on high variety and standards-compliant (e.g., HIPAA, common data model) distributed data sets that enable predictive analytics. Consequently, health information systems need to be developed using cooperation and distributed trust principles to allow protected data sharing between multiple domains or entities (e.g., health data service providers, hospitals and research labs). In this paper, we present a novel health information sharing system viz., HonestChain that uses Blockchain technology to allow organizations to have incentive-based and trustworthy cooperation to either access or provide protected healthcare records. More specifically, we use a consortium Blockchain approach coupled with chatbot guided interfaces that allow data requesters to: (a) comply with data access standards, and (b) allow them to gain reputation in a consortium. We also propose a reputation scheme for creation and sustenance of the consortium with peers using Requester Reputation and Provider Reputation metrics. We evaluate HonestChain using Hyperledger Composer in a realistic simulation testbed on a public cloud infrastructure. Our results show that our HonestChain performs better than the state-of-the-art requester reputation schemes for data request handling, while choosing the most appropriate provider peers. We particularly show that HonestChain achieves a better tradeoff in metrics such as service time and request resubmission rate. Additionally, we also demonstrate the scalability of our consortium platform in terms of the Blockchain transaction times.