Surgical robotic systems with miniaturized flexible Tendon-driven Serpentine Manipulators (TSM) have enjoyed increasing popularities among surgeons and researchers for their advantages of working in constrained and torturous human lumen such as oral cavity and upper GI tract. However, they suffer from sufficient nonlinearities and model uncertainties due to friction, tension varying, tendon slacking, etc. Model based control is insufficient to overcome such uncertainties and automate challenging surgical related tasks. The objective of this work is to automate certain clinical tasks to alleviate surgeon fatigue and promote task efficiency in kinematics free and sensor free circumstances. We present a data-driven approach based on Learning from Demonstration (LfD), which utilizes statistical machine learning models to encode system underlying dynamics and generalize smooth motor trajectories by direct actuation space learning. Motion segmentation is enabled with soft margin Support Vector Machine (soft-SVM) in complicated tasks. We also make attempts to retrieve task-specific properties by Locally Weighted Regression (LWR). We evaluated the approach on two surgical related tasks: compliant insertion and simplified Endoscopic Submucosal Dissection (ESD). The flexible TSM successfully reproduced both tasks and demonstrated superior trajectory performance. A video is available at: https://youtu.be/rLQo6xKtyMI.