The only way I'm making any sense of this is to assume the wire is bent onto a closed rectangle with the magnet in the center. In this case the net force on the closed loop is 0 due to the fact that we can always find a segment of the wire that has an opposing force on it.
But that doesn't make sense to me. Why even mention the current or the flux through the loop?
But if the wire is straight, then the magnetic flux is measured where? In reference to what? The force on different segments of the wire are going to be different. Unless the flux is to be presumed to be constant over all space?
I guess I'm saying I need more information here!