Bolted flange joints are indispensable components in process industries due to the good sealing, assemble and disassemble capacities. Generally, the flange rigidity characterized by the rotation angle is a key index to evaluate the sealing tightness of flange joints. However, the rotation angle of flange is usually too small (less than 1º) to monitor during the assemble and operation stages. Accordingly, a novel flexure magnifying mechanism is designed to measure the small rotation angle of flange joints under internal pressure and external bending moment. The magnification factor and calculation approach of the flexure amplification mechanism are deduced and verified by experimental data and finite element simulation. Results indicate that the proposed measuring apparatus has good performance to monitor the maximum rotation angle. It is of great interest that the measured location of the maximum rotation angle is in good agreement with that in the experiment, and the average error is 7.3%, which is acceptable for practical application. Additionally, the leakage rate at the top of flange joints slowly and almost linearly increases with the increment of external bending moment ascribing to the decrease the gasket stress near the top of flange joints.