Distributed machine learning approaches, including a broad class of federated learning (FL) techniques, present a number of benefits when deploying machine learning applications over widely distributed infrastructures. The benefits are highly dependent on the details of the underlying machine learning topology, which specifies the functionality executed by the participating nodes, their dependencies and interconnections. Current systems lack the flexibility and extensibility necessary to customize the topology of a machine learning deployment. We present Flame, a new system that provides flexibility of the topology configuration of distributed FL applications around the specifics of a particular deployment context, and is easily extensible to support new FL architectures. Flame achieves this via a new high-level abstraction Topology Abstraction Graphs (TAGs). TAGs decouple the ML application logic from the underlying deployment details, making it possible to specialize the application deployment with reduced development effort. Flame is released as an open source project, and its flexibility and extensibility support a variety of topologies and mechanisms, and can facilitate the development of new FL methodologies.