Contemporary lean thinking, especially in knowledge work areas like software engineering, begins with understanding flow. Architecture plays a vital role in enabling the flow of value in software engineering teams and organizations. To date there has been little research in understanding impediments to flow in software engineering organizations. A focus on enabling flow through removing impediments is a useful perspective in creating a more agile, lean thinking software engineering organization. Particularly so when supported by appropriate metrics. This paper presents a case study of how architecture-related impediments impact the flow of work in software engineering teams and organizations. The key contributions of this paper are centered on the concept of flow and impediments in modern software engineering, and its relationship with architecture. We develop an understanding of how a focus on flow and removing impediments, supported by appropriate metrics, is helpful in identifying architecture-related challenges. Drawing on research of one company's practices the paper presents an example of a scenario where flow analysis using specific metrics reveals architecture-related impediments and shows how addressing these impediments improves effectiveness and productivity in ways that would not otherwise have been revealed.