When we refinished out mast and replaced the standing rigging, the old flag halyard went in the garbage. The new ones were much simpler, with just an eye loop at the spreaders, and the halyards tied around the base of the stays.
I originally wanted to put a small cleat on the stay, but our riggers talked me out of it. They claimed it would trap dirt and salt that would prematurely age the stay. It is not really much harder to tie it around the stay turnbuckle, so that works for now.
I looked at several different clips for attaching burgees and flags, and was not happy with any of the spring-loaded ones. I did not have confidence that they would stay put. Instead, I bought some clips from Amazon and tied one to each end of the halyard. They attach directly to the grommets in our burgee.
If I want to add another flag, I just tie two more clips to a short line and put it between the two flags. There is never any issue with having the clips in the right place. I just string them together, hoist the whole set, then snug up the halyard and tie it off.
At the end of the day, I lower the flags, hook the clips together, remove the flags and tie it off. The burgees are stored below on a plastic clothes hanger made for pants.
