This study used the L-M (Levenberg-Marquardt) algorithm to analyze the fitting of the flexibility coefficient of fasteners in the mixed connection structure of metal composite materials to address key challenges in aircraft structural design. Through parametric modeling and finite element simulation of single lap joints, the system evaluates eight key factors, including the direction of the composite material layer, the elastic modulus of the metal plate, the plate thickness ratio, the fastener diameter, the elastic modulus of the fastener, the Poisson’s ratio of the fastener, the magnitude of the preload force, and the type of bolt configuration, covering convex and countersunk variants. Advanced material modeling techniques are introduced in the study to accurately capture the anisotropic behavior of the composite material layer and its interaction with metal components under different load conditions. The results show that the higher modulus and thickness of the composite material plate and metal plate significantly reduce the flexibility of fasteners, and larger fastener diameters are associated with reinforcement. The elastic modulus further reduces flexibility. The flexibility of convex head bolts is significantly lower than that of countersunk head bolts, while Poisson’s ratio, preload force, and humidity have little effect. Based on these findings, a new flexible calculation formula containing nine undetermined parameters is proposed. The L-M algorithm is used for nonlinear regression to derive formulas with physical significance. The verification shows that the proposed formula is highly consistent with the finite element results, with a corrected coefficient of determination of 0.956. Among 864 test sample points, 73.61% have an error of less than 5%, and only 0.23% have a deviation of more than 15%. Comparative analysis with twelve existing methods, including the Delft University and Boeing formulas, confirms that the proposed method has better accuracy. This method effectively expands the applicability of traditional flexible formulas, provides solid theoretical support for advanced aircraft connection design, and realizes diverse mixing in aerospace engineering and accurate calculation of connection configuration.