I'm a Board-Certified Avian Specialist (veterinarian). I work mostly with parrots/pet birds and certainly don't claim to be a chicken expert, but your question peeked my interest.
A quick google search revealed that "seaweed" contains about 70mg salt/cup. The recommended salt content in chicken feed is about 0.2% or about 2mg/ml of food. So a cup of feed contains about 500 mg salt, IF my calculations are correct. (I know liquid ml aren't the same as dry ml, so these calculations aren't perfect, which is why I'm not making any recommendations....but it seems like 70 mg of salt in a cup of seaweed would not be extreme). Certainly washing it with freshwater is a good idea as well as observing the chickens to see if they start drinking more water would be prudent. (Of course we don't know if there is anything besides excess salt in chaeto that might be harmful, though).
Again, I'm not recommending that you feed chaeto to chickens....just some interesting info to investigate further perhaps!
I wish you could give me some of your extra Chaeto! I just set up a refugium and my chaeto died in a few weeks. (I posted a thread on it earlier today; no responses though! :)