This paper proposes Federated Learning (FL) based smart healthcare system where Medical Centers (MCs) train the local model using the data collected from patients and send the model weights to the miners in a blockchain-based robust framework without sharing raw data, keeping privacy preservation into deliberation. We formulate an optimization problem by maximizing the utility and minimizing the loss function considering energy consumption and FL process delay of MCs for learning effective models on distributed healthcare data underlying a blockchain-based framework. We propose a solution in two stages: first, offer a stable matching-based association algorithm to maximize the utility of both miners and MCs and then solve loss minimization using Stochastic Gradient Descent (SGD) algorithm employing FL under Differential Privacy (DP) and blockchain technology. Moreover, we incorporate blockchain technology to provide tempered resistant and decentralized model weight sharing in the proposed FL-based framework. The effectiveness of the proposed model is shown through simulation on real-world healthcare data comparing other state-of-the-art techniques.