While visuomotor policy has made advancements in recent years, contact-rich tasks still remain a challenge. Robotic manipulation tasks that require continuous contact demand explicit handling of compliance and force. However, most visuomotor policies ignore compliance, overlooking the importance of physical interaction with the real world, often leading to excessive contact forces or fragile behavior under uncertainty. Introducing force information into vision-based imitation learning could help improve awareness of contacts, but could also require a lot of data to perform well. One remedy for data scarcity is to generate data in simulation, yet computationally taxing processes are required to generate data good enough not to suffer from the Sim2Real gap. In this work, we introduce a framework for generating force-informed data in simulation, instantiated by a single human demonstration, and show how coupling with a compliant policy improves the performance of a visuomotor policy learned from synthetic data. We validate our approach on real-robot tasks, including non-prehensile block flipping and a bi-manual object moving, where the learned policy exhibits reliable contact maintenance and adaptation to novel conditions. Project Website: https://flow-with-the-force-field.github.io/webpage/