Predictive modeling in high-stakes domains often suffers from limited observed features due to ethical and practical constraints. To address this challenge, we propose a novel approach that formulates latent feature mining as a text-to-text propositional logic reasoning task, facilitating domain knowledge integration and improving the interpretability of latent features. We design FLAME, a domain knowledge-augmented reasoning framework for latent feature mining, offering an efficient training paradigm to strengthen the domain-specific reasoning capabilities of large language models (LLMs) for latent feature extraction. The goal of our framework is to augment observed features with inferred latent features, enhancing the performance of predictive models in downstream machine learning tasks. We validate our approach through two case studies: (1) the criminal justice system, where data collection is ethically challenging and inherently limited, and (2) the healthcare domain, where patient privacy concerns and the complexity of medical data restrict comprehensive feature collection. Experimental results demonstrate that the inferred latent features significantly enhance the performance of downstream classifiers by over 10%.