People with a sick chicken in pain that want to end the life without further pain are probably not interested in eating the chicken.
In the other topic about euthanising a chicken someone mentioned gassing in an airtight box.
If @Maiahr wants to eat the chicken I think its fine to kill the...
This thread is about euthanising a sick chicken humanly without pain. https://www.backyardchickens.com/threads/how-to-euthanize-a-chicken-humanely.1561319/page-4#post-27480194