It is very difficult to give an answer somebody can't find a detail or 2 to add. If the old flex isn't plastic coated, replace it. In addition to the ring, the plastic coating is sort of a notice of being the newer, more reliable design. The older designs could eventually crack causing a gas leak.
A little more on the fittings. At least one end of the flex will have a flared fitting. Pipe seals by screwing a tapered thread into another tapered thread. SAE and JIC flare fittings use straight threads to draw a flared tube down on a cone shaped seat. So as Let said, look for the adapter. I am only adding a couple of details to the correct procedure above that you should follow.