The advancement of flexible Al-air batteries demands high-performance, non-precious oxygen reduction reaction (ORR) catalysts and compatible solid-state electrolytes to achieve high power output, stability, and mechanical resilience. Herein, we present an innovative and novel approach to synthesize a high-performance, non-precious ORR catalyst by covalently grafting a carboxyl group containing Fe-based ionic liquid (Fe-IL), 1-(3-carboxybutyl)-3-methylimidazolium tetrachloroferrate ([CBMIM][FeCl4]), onto a zirconium (Zr)-based metal-organic framework (MOF), UiO-66-NH2, via amide bond formation. This molecular-level integration ensures uniform Fe distribution, suppresses agglomeration during pyrolysis, and leads to a nitrogen-doped carbon matrix embedded with ZrO2 nanodomains and atomically distributed Fe-Nx sites. The optimized FeZrO2-NC (850) catalyst exhibits a high onset potential (Eonset) (0.98 V vs. RHE) with a half-wave potential (E1/2) of 0.91 V vs. RHE and superior stability, exceeding the commercial Pt/C. Complementing the catalyst, we develop a novel quasi-solid-state electrolyte based on a cationic polyelectrolyte gel embedded in a polypropylene (PP) pad, delivering leak-proof operation with high ionic conductivity and mechanical flexibility. When integrated into a flexible Al-air battery, the device delivers an open-circuit voltage (OCV) of 1.47 V with a peak power density of 42 mW cm-2 and maintains stable operation under mechanical deformations. This work highlights the synergistic integration of ionic-liquid-functionalized MOFs and quasi-solid-state electrolytes, establishing a scalable route toward next-generation flexible aluminum-air batteries (FAABs).