Any spiral metal flexible conduit (such as BX) does not itself qualify as the equipment grounding conductor unless it has a bare wire or metal strip running lengthwise inside but outside any paper lining. This strip does not have to come into metal boxes and be wire nutted to other ground wires. A common way of dealing with it is to fold it back (if it protrudes that far from the end) and clamp the conduit to the box with the strip hanging outside the box.
Meanwhile a green wire running in the conduit, flexible or otherwise, may only be used as an EGC.
For plastic boxes, an EGC running inside conduits (and cables) and entering the box to be wire nutted to other EGCs is required. A bonding wire that comes inside a flexible conduit can be used for this if it is of adequate size e.g. #12 gauge copper for 20 amp circuit. Each circuit sharing a conduit does not need its own EGC provided that the EGC that is there is sized for the highest amperage circuit.
I am not sure whether there exist any situations where metal conduit and metal boxes are bonded as an equipment ground but there is another completely separate equipment grounding system consisting of (green) insulated ground wires accompanying the current carrying conductors in the conduits. Medical applications mentioned previously might be such situations.
When the mounting strips (yokes) of receptacles, switches, etc. are screwed to the (metal) boxes in this situation, the result will be a redundant grounding as opposed to two separate grounding systems even though simply screwing receptacles, etc. to metal boxes does not eliminate the need to run EGCs (using pigtails, etc.) to both the box and the receptacle, etc. in other situations such as residential.