Structural parameters decide the amplification, gain, and motion accuracy of the flexible micro-displacement amplification mechanism. However, research on the structural parameters of the flexure hinge or flexible amplification mechanism is still sparse. In order to optimize the flexible amplification mechanism, it was necessary to design the flexure hinge and flexible amplification mechanism parametrically. In this context, a new general structural parameter ε was proposed. Its effect on the flexibility coefficients of different types of flexure hinges was discussed in detail, and the flexibility features of commonly used flexure hinges were compared horizontally. Based on the analysis of the flexibility features, a new parameter λwas proposed as the flexibility ratio, and the main types of output displacement sensitivities of the flexure hinges with different λwere analyzed. A practical bridge-type flexible micro-displacement amplification mechanism was taken as an example, which achieved the parametric design with εandλ, and was also simulated for parametric design using the finite element method (FEM). After parametrically designing the flexible amplification mechanism based on flexure hinges, combined with theεandλparameters, the experimental results showed that the error of the output displacement between FEM and experiment was only 3.80%. It was thus feasible to design a flexible amplification mechanism parametrically using the structure parameters of the flexure hinges, and such design is helpful to optimize this type of flexible amplification mechanism.