Thin-walled shells, as crucial load-bearing components in major equipment, are preferred over thin plates due to compactness, aesthetics, and mechanical performance. When machining thin plates, issues caused by chatter, such as low accuracy and accelerated tool wear, often arise. Curved surfaces exacerbate these difficulties and place higher demands on the adaptability of fixtures. To solve this problem, we propose a composite flexible fixture (CFF) integrated with magnetic follow-up support technique for milling curved workpieces for the first time. The flexible clamping mechanism, constructed by independent support heads with embedded torsion springs, resolves the inherent trade-off in rigid fixtures between clamping stability and surface adaptability. The slide rail-slider mechanism extends the curvature radius adaptation range to 0.5-1.5 m. Quantitative analysis demonstrates that CFF enhances workpiece damping ratio and stiffness by 91 % and 10 %, respectively, resulting in a reduction of over 90 % in response amplitude. Based on model order reduction and harmonic balance method, an efficient solving strategy is established for dynamic analysis of the milling system, significantly reducing calculation costs. In mirror milling experiments, the root mean square of the acceleration signal reduces by 91.42 %, with roughness decreasing by 50.44 %. CFF effectively mitigates the impacts of curvature and milling positions on machining results, serving as an optimal auxiliary device for large-scale curved thin-walled workpieces.