COVID-19 has spread rapidly across the globe and become a deadly pandemic. Recently, many artificial intelligence-based approaches have been used for COVID-19 detection, but they often require public data sharing with cloud datacentres and thus remain privacy concerns. This paper proposes a new federated learning scheme, called FedGAN, to generate realistic COVID-19 images for facilitating privacy-enhanced COVID-19 detection with generative adversarial networks (GANs) in edge cloud computing. Particularly, we first propose a GAN where a discriminator and a generator based on convolutional neural networks (CNNs) at each edge-based medical institution alternatively are trained to mimic the real COVID-19 data distribution. Then, we propose a new federated learning solution which allows local GANs to collaborate and exchange learned parameters with a cloud server, aiming to enrich the global GAN model for generating realistic COVID-19 images without the need for sharing actual data. To enhance the privacy in federated COVID-19 data analytics, we integrate a differential privacy solution at each hospital institution. Moreover, we propose a new blockchain-based FedGAN framework for secure COVID-19 data analytics, by decentralizing the FL process with a new mining solution for low running latency. Simulations results demonstrate the superiority of our approach for COVID-19 detection over the state-of-the-art schemes.