Developing imaging models capable of detecting pathologies from chest X-rays can be cost and time-prohibitive for large datasets as it requires supervision to attain state-of-the-art performance. Instead, labels extracted from radiology reports may serve as distant supervision since these are routinely generated as part of clinical practice. Despite their widespread use, current rule-based methods for label extraction rely on extensive rule sets that are limited in their robustness to syntactic variability. To alleviate these limitations, we introduce RadPert, a rule-based system that integrates an uncertainty-aware information schema with a streamlined set of rules, enhancing performance. Additionally, we have developed RadPrompt, a multi-turn prompting strategy that leverages RadPert to bolster the zero-shot predictive capabilities of large language models, achieving a statistically significant improvement in weighted average F1 score over GPT-4 Turbo. Most notably, RadPrompt surpasses both its underlying models, showcasing the synergistic potential of LLMs with rule-based models. We have evaluated our methods on two English Corpora: the MIMIC-CXR gold-standard test set and a gold-standard dataset collected from the Cambridge University Hospitals.