One way to manage textile wastes may be their two-stage utilization in the process of co-pyrolysis with waste tires, followed by gasification of the resulting char. Therefore, the steam gasification process of chars obtained in the co-pyrolysis of rubber from used tires with the addition of cotton and polyester (in the amounts of 0, 25, 50, and 75%) was investigated. Gasification measurements were performed in a fixed-bed reactor under isothermal conditions (800, 850, 900, and 950 °C), at a pressure of 1.0 MPa, using the thermovolumetric method. Based on the obtained results, the curves of the formation rates of the main gas components (CO, H2, CO2, and CH4) as well as the curves of the conversion degree (with reactivity indexes R(x)) were developed. Moreover, based on the gaseous product yields, the gas composition was assessed. Kinetic parameters of the gasification reaction were also calculated using two approaches (Random Pore Model and Isoconversional Method). The addition of cotton and increasing its amount has a beneficial effect on the gasification process, resulting in higher reaction rates, higher conversion degrees, and improved kinetic parameters. The addition of polyester usually also improves the gasification process, although to a much lesser extent than cotton. The analysis of the composition of the resulting gas showed that in the case of blends with the addition of polyester, a hydrogen-rich gas was obtained, while blends containing cotton favor the formation of both CO and H2. Overall, the obtained results clearly indicate the possibility of conversion of char obtained during co-pyrolysis of rubber and textile waste into high-value synthesis gas by gasification.