Healthcare interoperability unfolds the way for personalized healthcare services at a reduced cost. Furthermore, a decentralized system holds the promise to prevent compromises such as cyber-attacks due to data breaches. Hence, there is a need for a framework that seamlessly integrates and shares data across the system stakeholders. We propose SENSIBLE, a blockchain-powered, knowledge-driven data-sharing framework that gives patients complete control of their medical history and can extract rich information hidden in it using knowledge graphs (KGs). By incorporating both blockchain and KGs, we can provide a platform for secure data sharing amongst stakeholders by maintaining data privacy and integrity through data authentication and robust data integration. We present a Proof-of-Concept of the SENSIBLE network with Ethereum to share dynamic knowledge across stakeholders. Dynamic knowledge generation on the blockchain provides a two-fold advantage of cooperation and communication amongst the stakeholders in the healthcare ecosystem. This leads to operational ease through sharing relevant portions of complex information while also ensuring the isolation of sensitive medical data.