I believe the equipment grounding conductor must be run inside the flex however an equipment bonding jumper can be run on the outside. When using sealtight or LFMC with service conductors as allowed in 230.43(15) then an equip. bonding jumper must be used. The jumper must be sized to T. 250.66 thus it can be large and may need to be on the outside because of space limitations.- art. 250.102 will discuss the EBJ.