Robot-assisted minimally invasive surgery (MIS) using flexible endoscopy has emerged as a groundbreaking technology for improving traditional surgical approaches. However, a major challenge in advancing this technology is the lack of shape sensing, which leads to inaccurate navigation and control of ultra-long flexible endoscopy within the narrow and tortuous lumen environment. The unique characteristics of flexible endoscopy, including large slenderness ratio, high bending angles, and non-symmetric, multi-channel configurations, pose significant challenges to accurate shape sensing. To address this challenge, we propose a novel shape-sensing scheme based on distributed fiber optic strain measurement, which incorporates a complete and applicable multi-interface strain transfer model adapted to large deformation and multiple sensing points. To validate the theoretical model, a shape sensor with a diameter of 2.84 mm and a length of 500 mm is fabricated. Both 2D and 3D shape sensing experiments are conducted on predefined templates, and the results highlight a significant improvement in the precision of sensor measurements through the utilization of the proposed model. Specifically, the 3D experiment results show a mean absolute error (MAE) of 5.38 mm for complex geometrical shapes and the proposed model reduces the MAE by approximately 52.9% compared to the unmodified case.