We present Streami, an extensible GPU-accelerated library for the computation of field lines in fluid flows on high-performance computers. Streami acts as a thin layer used for both post-hoc or in-situ analysis and can interface with existing MPI applications. We discuss Streami's application programming interface, key design decisions that led to Streami's high performance and extensibility, as well as extensions to support different fluid flow field representations. We also present a sample application for rapid prototyping and interactive seed point placement. Streami is released under a permissive open-source software license.