Wind farm flow control (WFFC) is a promising technology for improving wind farm operation and design. The presented study focuses on the combination of the two most prominent WFFC strategies, yaw-based wake-steering and axial induction control via constant blade pitch, for maximising the wind farm power production with and without a load constraint. The optimisation is performed via data-driven polynomial-based probabilistic surrogate models, calibrated through a range of LES and aeroelastic simulations for a 2-turbine setup. The results indicate the yaw-based wake-steering to be the driving mechanism to increase the wind farm power production, particularly when loads are not considered. However, axial induction is seen beneficial for load alleviation, especially in close spacings. Overall, the analyses highlight the potential of combined WFFC strategies for power optimisation in a safety-critical system and provides a probabilistic approach for data-driven multi-objective farm flow control.