This paper presents a novel interval type-2 TSK nominal-fuzzy-model-based sliding mode controller (IT2-TSKNFMSMC) for flexible air-breathing hypersonic vehicle (FAHV) in order to stress robustness of the control system in dealing with data-driven based fuzzy modelling deviations, system uncertainty and disturbances. We adopt backstepping structure decomposing FAHV model into 5 control subsystems and design controllers, respectively. More specifically, two subsystems are designed with integral sliding mode model controllers. Another three subsystems which directly coupling with flexible mode disturbances are designed with IT2-TSK-NFMSMCs by the following steps: 1) interval type-2 TSK nominal-fuzzy-models (IT2-TSK-NFM) are generated automatically by using type-2 fuzzy self-organizing methods from experiment datasets; 2) nominal model sliding mode controllers are designed based on the IT2-TSK-NFM, respectively; 3) notch filters  are adopted in order to decrease the disturbance effects from the flexible modes; 4) sliding mode compensation controllers are designed through Lyapunov synthesis in order to compensate differences between IT2-TSK-NFM and real models of the FAHV. Several scenarios are studied and the simulation results validate the robustness of the proposed controllers when there exist internal flexible vibration and external system disturbances.