In this paper, we propose a Machine Learning (ML) based approach to address Wireless Channel Estimation (WCE) problem for 5G and beyond wireless networks. Accurate wireless channel estimation plays a crucial role for provision of high quality of service to billions of wireless devices in current and future wireless networks. Our proposed approach uses contemporary ML technique, Federated Learning (FL), in conjunction with the Stochastic Gradient Descent (SGD) algorithm to optimise the WCE problem. Our proposed approach leverages the local user wireless channel information to locally optimise the objective at users and then uses this locally optimised information at the server to optimise the global objective function. The proposed approach is referred to as joint Federated Server Learning and Federated Client Learning (j-FSL-FCL) in the paper. We formulate the WCE problem with a novel loss function to be used for the optimisation problem. To evaluate the performance of our proposed j-FSL-FCL approach (with and without SGD), we consider a Down Link (DL) wireless channel model with Multiple-Input Multiple-Output (MIMO) setting that mimic closely to the wireless channel for 5G and beyond wireless channel models. The performance measuring parameters for j-FSL-FCL are to minimise the difference between actual and estimated wireless channel parameters (channel strength and direction). We compare the results of our proposed approach with the other techniques in the literature based on Least Squares (LS), Linear Regression (LR) and Mean Square Error (MSE). It is shown that the proposed algorithm converges to the optimal solution quickly when used with SGD compared to other existing techniques. It is also shown that the efficiency of the proposed approach for WCE problem is much higher compared to other LS and MSE based techniques. Finally, we present some interesting futuristic applications of FL in the context of 5G and beyond wireless networks.