Does magnetic flux depend on the orientation of the ferromagnetic rotor?
In general, magnetic flux depends to some extent on the angular position of the rotor for all motors. The extent of dependance depends on the motor design. In induction motors, the stator and rotor are designed to minimize that effect.

Reluctance motors use that effect as a principal of operation. As the stator magnetic field rotates, the rotor turns to remain aligned in the orientation of minimum reluctance. If the torque required to maintain speed is constant, the angular position of the rotor with respect to the rotating field is constant, and the reluctance is constant. If the load increases of decreases, the torque angle, reluctance, magnetic flux and current all change to accommodate the torque change.