In emergency departments, rural hospitals, or clinics in less developed regions, clinicians often lack fast image analysis by trained radiologists, which can have a detrimental effect on patients' healthcare. Large Language Models (LLMs) have the potential to alleviate some pressure from these clinicians by providing insights that can help them in their decision-making. While these LLMs achieve high test results on medical exams showcasing their great theoretical medical knowledge, they tend not to follow medical guidelines. In this work, we introduce a new approach for zero-shot guideline-driven decision support. We model a system of multiple LLM agents augmented with a contrastive vision-language model that collaborate to reach a patient diagnosis. After providing the agents with simple diagnostic guidelines, they will synthesize prompts and screen the image for findings following these guidelines. Finally, they provide understandable chain-of-thought reasoning for their diagnosis, which is then self-refined to consider inter-dependencies between diseases. As our method is zero-shot, it is adaptable to settings with rare diseases, where training data is limited, but expert-crafted disease descriptions are available. We evaluate our method on two chest X-ray datasets, CheXpert and ChestX-ray 14 Longtail, showcasing performance improvement over existing zero-shot methods and generalizability to rare diseases.