This paper is mainly dedicated to the challenging issue of fixed-time attitude control for a flexible spacecraft in the presence of actuator faults, external disturbances and coupling effect of flexible modes. The attitude controller is developed by employing a fixed-time nonsingular terminal sliding mode under which the convergence time is bounded and independent of the initial states. This robust attitude controller is able to provide superior properties such as fast fixed-time attitude manoeuvring with high pointing accuracy, singularity avoidance and chattering free. More specifically, a new reaching law is employed to provide convergence rate improvement as well as chattering alleviating simultaneously. The actuator fault problem is also considered and the attitude control is achieved even when the actuators experience severe faults. The proposed controller ensures that the closed-loop attitude system is stable in the sense of fixed-time stability concept. Furthermore, since the upper bound of external disturbances and flexible vibrations acting on the spacecraft is not available, an adaptation mechanism is presented. Numerical simulations demonstrate that the proposed controller is able to successfully accomplish attitude control with high attitude pointing accuracy and stability in spite of the actuator faults, flexible structures vibrations and external disturbances.