I have no idea experience wise, but it seems that if you are using boro It could be done the same way as making jump rings in metal, conceptually. Make a spiral of boro around a cold pipe or mandrel. Something that is the diameter that you want your rings to be. (i think i have read that it should not bond to to metal.) Then when cool you can nip the rings, and then just close them up in the flame with some tool to hold them. or pliers or jax or something. It seems like this would be easier than trying to make each circle alone, then open and close them. I would be interested if this works or not. I do not work in boro. I am just making it up, based on things I have read, and my soft glass work.
You may also try searching/asking in the boro room