In the field of cognitive healthcare Internet of Things (CH-IoT), there is a strong demand for reliable and minimally intrusive smart gadgets that consistently acquire, analyse, and obtain the confidential health details of the individual. In fact, CH-IoT is empowered with artificial intelligence (AI) to transmute a fewer operational inputs into actionable, intelligent actions through the digitization of medical healthcare data. However, these systems consume more network complexity, interaction, and overhead costs, while inducing a blend of susceptibility and confidentiality issues. In support of this complexity, these cognitive systems need centralised data collection and to be gathered and analysed, which affects scalability issues and adds fuel to privacy and security breaches. Even though it possesses greater intricacy in its potential application, a substantial factor is maintaining the private preservation of healthcare data against the growing attacks. Thus, this paper presents a distributed privacy-preserving, chaotic encryption-based framework that can be deployed for CH-IoT systems to safeguard sensitive data against message modification, denial of service (DoS), and man-in-the-middle attacks (MIM), guaranteeing privacy and data integrity. The proposed framework integrated the federated learning layered hybrid chaotic encryption strategies by investigating through examination the learning infrastructure of convolutional neural networks (CNN). In the examination, the complete framework was carried out in the Tensorflow Federated Learning Libraries (FLL), and numerous performance metrics such as accuracy, precision, recall, f1-score, transmission efficiency, and overhead ratio were measured and contrasted with the various existing frameworks. For the intensive analysis, formal and informal security experiments were also conducted by NIST (National Institute of Science and Technology). The analytical results illustrate the importance of the proposed framework by achieving better security performance and outperforming the other existing models. Lastly, the proposed framework has more potential than the other existing frameworks and finds its place in real-time healthcare systems, but it needs to be improvised for real-time datasets.