This paper presents an extensible highly compact fiber-optic system for multi-segment flex sensing. This fiber-optic arrangement is 7.5 mm in diameter and is comprised of a flexible and stretchable Steiner chain (n=12) housing at the top which accommodates passive cables used for sensing, followed by a basal rigid fiber-optic sensing unit. The U-shape loopback design of the sensing system allows integration of electronics on one side and away from the sensing region. A low-friction retractable distance modulation array is designed and implemented to reduce the hysteresis and recover reference sensor values when the arm returns to its original straight configuration. This sensing system is able to measure the dynamic flex patterns of the actuation system to which it conforms. This sensing system can also be embedded inside soft robotic manipulators for multi-segment flex sensing independent of actuation systems, temperature or external load from the environment. This arrangement can also be used as a complete manipulation system when actuating tendons are attached.