It does sound like poison to me. I have treated botulism in chickens, it starts off like a drunken-ness, then it is full body paralysis. Unless they ate maggots, or had access to anaerobic decomposting organic matter, that is unlikely. You don't have to buy activated charcoal, you can make your own by burning clean wood, yes charcoal will absorb toxins and is natural.
It has to be diet related, so if you are sure they are getting a well balanced feed or mix, then it could have been a something accidental ingested. You can do an autopsy and examine the intestinal tract in the future. As long as you are sure their diet is well rounded and nutritiously balanced feed, if not try adding another food type.
But to me the likely culprit is cocci. Check out this thread.
https://www.backyardchickens.com/threads/very-sick-duck-coccidiosis.698008/
Unfortunately you would have to have a script from a doc in the united states for those meds.