The 2x10 floor joist in right in the middle of where I want the center of the flange to be, how much of the floor joist can I legally remove so the offset flange will fit?

If it is right in the center and offset will not help you much. You either need to change your desired placement or open up a larger opening in the floor and add double cross bracing to the adjoining joists ( it would look like a herader around a window in a load bearing wall)