'Cord backs will not work on 'Flexes. They do not have the part that presses on the Automat system trigger when you close the back.
A quick test says that a 'Flex back will fit a Rolleicord. Although the latches on the backs are different, I bet that they are in the same location, with the mechanism being different ways to accomplish the same thing. The Automat tab will clear the film roll.
Later 'Flex backs have tabs and such to lock the film spools, press other sensors, etc. Beyond my knowledge to lay out the variations.
Early stuff, plate film backs, etc., no idea.
momus has it right- dented backs may still work fine. If it doesn't leak light. The film pressure plate is indexed to the body itself, not to the back, so if the back closes, the pressure plate will be fine.