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In this paper, we show how the Federated Learning (FL) framework enables learning collectively from distributed data in connected robot teams. This framework typically works with clients collecting data locally, updating neural network weights of their model, and sending updates to a server for aggregation into a global model. We explore the design space of FL by comparing two variants of this concept. The first variant follows the traditional FL approach in which a server aggregates the local models. In the second variant, that we call Flow-FL, the aggregation process is serverless thanks to the use of a gossip-based shared data structure. In both variants, we use a data-driven mechanism to synchronize the learning process in which robots contribute model updates when they collect sufficient data. We validate our approach with an agent trajectory forecasting problem in a multi-agent setting. Using a centralized implementation as a baseline, we study the effects of staggered online data collection, and variations in data flow, number of participating robots, and time delays introduced by the decentralization of the framework in a multi-robot setting.