Statically analyzing information flow, or how data influences other data within a program, is a challenging task in imperative languages. Analyzing pointers and mutations requires access to a program's complete source. However, programs often use pre-compiled dependencies where only type signatures are available. We demonstrate that ownership types can be used to soundly and precisely analyze information flow through function calls given only their type signature. From this insight, we built Flowistry, a system for analyzing information flow in Rust, an ownership-based language. We prove the system's soundness as a form of noninterference using the Oxide formal model of Rust. Then we empirically evaluate the precision of Flowistry, showing that modular flows are identical to whole-program flows in 90% of cases drawn from large Rust codebases. We illustrate the applicability of Flowistry by implementing both a program slicer and an IFC checker on top of it.