Sewing flexible materials such as textiles and clothing can be challenging due to their tendency to wrinkle easily and their non-linear mechanical behaviour. Conventional methods in industrial plants are performed by workers and can be labour-intensive and time-consuming. Therefore, the interest in robotic solutions has grown in the last decade. In this paper, we propose a flexible and reliable robotic solution that can autonomously remove wrinkles from fabric. This method was designed as a part of a robotic cell capable of sewing together two different textiles, used in the manufacturing of cyclist garments. The robotic system employs two compliant soft fingers to stretch the fabric and a vision system to identify the wrinkles to flatten. The design of the fingers is bio-inspired, mimicking the adaptability and dexterity of biological systems, hence improving the gripping performance while reducing the risk of damage to the fabric. The developed vision system performs instance segmentation to identify the wrinkles on the fabric, and then identifies the best places to apply the gripper to flatten the tissue. This two-step process is iterated until wrinkles on the surface do not affect the final sewn product. Such a methodology is highly flexible and has no hard requirements, as the vision system requires only an RGB camera, and the fingers are 3D-printed, an affordable and common manufacturing process. Consequently, the system proposed in this paper can be easily employed in a wide variety of industrial scenarios, improving the productivity and the welfare of the workers.