Using Fleming's right-hand rule, in which direction will the current flow if the direction of magnetic field is towards north and the conductor is moving vertically upward?

According to Fleming's right-hand rule, arrange the thumb, forefinger, and middle finger of the right hand mutually perpendicular to one another:
Thumb points in the direction of the movement of the conductor (Upward).

Forefinger points in the direction of the magnetic field (North).

Middle finger points in the direction of the induced current.

By aligning your right hand such that the thumb points up and the forefinger points North (away from you), your middle finger will point towards the right side, which represents the East direction.