Data-driven Machine and Deep Learning (ML/DL) is an emerging approach that uses medical data to build robust and accurate ML/DL models that can improve clinical decisions in some critical tasks ($e.g.,$ cancer diagnosis). However, ML/DL-based healthcare models still suffer from poor adoption due to the lack of realistic and recent medical data. The privacy nature of these medical datasets makes it difficult for clinicians and healthcare service providers, to share their sensitive data ($i.e.,$ Patient Health Records (PHR)). Thus, privacy-aware collaboration among clinicians and healthcare service providers is expected to become essential to build robust healthcare applications supported by next-generation networking (NGN) technologies, including Beyond sixth-generation (B6G) networks. In this paper, we design a new framework, called HealthFed, that leverages Federated Learning (FL) and blockchain technologies to enable privacy-preserving and distributed learning among multiple clinician collaborators. Specifically, HealthFed enables several distributed SDN-based domains, clinician collaborators, to securely collaborate in order to build robust healthcare ML-based models, while ensuring the privacy of each clinician participant. In addition, HealthFed ensures a secure aggregation of local model updates by leveraging a secure multiparty computation scheme ($i.e.,$ Secure Multiparty Computation (SMPC)). Furthermore, we design a novel blockchain-based scheme to facilitate/maintain the collaboration among clinician collaborators, in a fully decentralized, trustworthy, and flexible way. We conduct several experiments to evaluate HealthFed; in-depth experiments results using public Breast Cancer dataset show the efficiency of HealthFed, by not only ensuring the privacy of each collaborator's sensitive data, but also providing an accurate learning models, which makes HealthFed a promising framework for healthcare systems.