These days, the usage of machine-learning-enabled dynamic Internet of Medical Things (IoMT) systems with multiple technologies for digital healthcare applications has been growing progressively in practice. Machine learning plays a vital role in the IoMT system to balance the load between delay and energy. However, the traditional learning models fraud on the data in the distributed IoMT system for healthcare applications are still a critical research problem in practice. The study devises a federated learning-based blockchain-enabled task scheduling (FL-BETS) framework with different dynamic heuristics. The study considers the different healthcare applications that have both hard constraint (e.g., deadline) and resource energy consumption (e.g., soft constraint) during execution on the distributed fog and cloud nodes. The goal of FL-BETS is to identify and ensure the privacy preservation and fraud of data at various levels, such as local fog nodes and remote clouds, with minimum energy consumption and delay, and to satisfy the deadlines of healthcare workloads. The study introduces the mathematical model. In the performance evaluation, FLBETS outperforms all existing machine learning and blockchain mechanisms in fraud analysis, data validation, energy and delay constraints for healthcare applications.