There are a lot of ideas out there that might work sometimes but really, you need poison and the only ant you have to poison is the queen. Since she's far underground you have to use a poison that her underlings will deliver to her. That's Amdro.
If you can find the nest, follow the directions and sprinkle it around, not on, the mound. If you can't then you'll have to put it where they will find it. It's not especially toxic to chickens but putting it in the coop doesn't sound good. You could make containers that the chickens wouldn't get into.
Chickens will eat fire ants but if the nest is someplace where a chicken can disturb it - that could turn out badly for the chicken if it got swarmed. I assume you know what happens if you put a stick or your foot into a fire ant mound. You're sure these are fire ants and not another kind?
Sevin is also not too toxic to chickens or humans and you can put it in crevices if you have to. I don't like to use poisons and you sound like you don't but sometimes it's better not to mess around. One non-toxic thing you can try is to sprinkle lots of DE (diatomaceous earth) around the coop. It might help keep ants out of the coop but is not a long-term solution. Remember, fire ants are invasive. They do not need to co-exist in your environment.
