This paper presents a mixed-signal feature-classifier co-design framework for the design of flexible front-end (FE) systems for wearable healthcare devices. Unlike existing FE solutions that focus solely on the classifier, this study takes a system-wide approach to address area and power constraints in ML-based healthcare systems by integrating an analog front-end, feature extraction, and classifier. Specifically, we design an analog feature extractor for the first time in FE, significantly reducing feature extraction costs, and enable application-specific designs through a hardware-aware NAS-based feature selection strategy. Healthcare benchmark evaluations demonstrate the implementation of a high-precision, ultra-low-area, and efficient flexible system, making it suitable for disposable, low-power wearable monitoring.