Application of flexible robotic systems and teleoperated control recently used in minimally invasive surgery have introduced paradigm shift in interventional surgery. While Prototypes of flexible robots have been proposed for surgical diagnostic and treatments, precise constraint control models are still needed for flexible pathway navigation. In this paper, a deep learning based kinematics model is proposed for motion control of flexible robots. Unlike previous approach, this study utilized the different layers of deep learning system for learning the best features to predict the damping value for each point in the robot's workspace. The method uses differential Jacobian to solve IK for given targets. Optimal damping factor that converges precisely around given target is rapidly predicted by a DNN. Simulation of the robot and implementation of the proposed control models are done in V-rep and Python. Validation with arbitrary points shows the deep-learning approach requires an average of 26.50 iterations, a mean error of 0.838, and an execution time of 3.6 ms for IK of single point; and converges faster than other existing methods.