Quote: That's more or less it --- do something to stop them making the sound, and break the pattern. It becomes a habit, so it takes a little bit to break it.
When I was in the vicinity and one or more chooks started the panic song, I'd do something along the lines of loudly say "ah-ah!" (same sound I tell the dogs off with) and clap my hands. This generally startled them into silence, but they'd usually start again, and then I'd make a quick beeline toward the chicken that started it. A mock charge like the alphas do to the subordinates. That usually startled them into silence again, but this time they usually took the hint. Soon it was enough to quietly say "ah-ah" in a warning tone if one started, and it'd shut up, and none of the others would take up the chorus.
This won't necessarily work for all chickens, they're all different, but it worked for almost all of mine. I did end up culling those that would not quit. But at least the rest of the flock trained out of it ok. Chickens can understand if they're being punished for something, so they didn't become afraid of me, and they were still friendly and trusting in general... Just those odd spacky ones which I would have culled anyway, always troublesome. If you speak to them and the cause and effect is obvious they'll understand. Some won't want to listen but those ones you'll have to deal with differently. Some chooks are quite stupid, others quite smart.
Generally there's always one who starts it and keeps restarting it. I targeted that one, or ones, since all the other chickens are watching, and are smart enough to put two and two together and thus realize that a chicken beginning to scream for no good reason gets run off by the human. Anyway, if the chicken didn't stop there (since some of the spackier hens would run off still making the noise at the top of their lungs) I would herd her into the cage and catch her and isolate her for a little while. (Calm-down/time-out sort of thing). When the issue progressed to the extent that they were all going off nonstop all day every day I'd throw very light things at the starters. Nothing that would hurt them but pretty quickly they understood they'd better not stand around the house yard or paddock and yell over nothing.
This was an isolated phase that's only occurred once, thankfully. My methods may not work for you, but whatever you try I hope it works. The nonstop sound of chicken alarm calls can be nerve grating.