Aiming at an aerospace flange clamp part, a hydroforming process of 1Cr18Ni9 stainless steel tubing was investigated to study the effects of single-process direct forming and dual-process forming on the part’s thinning rate and stick modulus. The results show that the tube forming process, i.e., the closing distance and preforming pressure, affects the material flow and has a great influence on the final forming results. In single process, the small deformable space of the tube is not favorable to the material flow, resulting in excessive thinning and cracking. The closing distance and low-pressure preforming stage of the dual-process can promote material flow. However, small closing distances and preform pressures can result in insufficient material flow and poor stick modulus. Selecting a larger closing distance and preform pressure results in excessive flange deformation leading to warpage. Through optimization simulations, it is determined that flange clamp parts could be successfully manufactured when the closure distance was 10 mm, the expansion pressure was 25 MPa, and the molding pressure was 150 MPa.