A team of researchers built PrivacyFlow, a framework that follows how personal information moves through an AI agent's actions and flags when that movement creates privacy risk. The framework draws on information-flow analysis, a technique from security engineering, and applies it to the multi-step action sequences that agents execute. Tested across several large language models and a purpose-built benchmark, the framework surfaced a sharp tradeoff: agents that act with less human oversight create more opportunities for private data to reach unintended destinations. The empirical results give product teams something rare: a measured signal for when an agent should pause and ask a human to decide, rather than proceeding. The framework distinguishes between data that is sensitive on its own (a medical record) and data that becomes sensitive through combination or destination (a name sent to a third-party service without consent). That distinction matters for anyone designing the moment a human reviews what an agent is about to do. For UX leads, the core finding is that privacy risk is not uniform across an agent's run. Some actions carry negligible risk; others carry enough that the cost of an interruption is worth it. PrivacyFlow offers a principled basis for deciding which is which, so the human sees a prompt at the right moment rather than after the fact.