If I click "reply" to your post it quotes the whole thing.
Then if I start typing somewhere in the middle of the quote, it usually breaks up the quoted part into sections at that point. I don't know why it is "usually" instead of always, because sometimes it does weird things, but it mostly works as a way to respond to one part and another.
This isn't directly about chickens as ESA animals, but here is a thread where someone talks about taking some chickens out in public:
https://www.backyardchickens.com/threads/ambassadors-for-the-farm.407880/
Perhaps that thread, or other posts/threads by the same person, will give some ideas that could help you.
A thing to be wary of, the internet has lots of wrong information about chickens as well as lots of correct information. When there is lots of information saying that something is a great idea, and not much about how to do it, I wonder how much actual experience any of them have. It's easy for people to copy each other in saying "this is a great idea..." without knowing if it even works.
For what you have read, if any of it comes from people who personally have ESA chickens, you might try asking them directly about the training and socializing.
For the chicken-keeping details I do know, the internet has a lot of wrong information being repeated from one site or blogger to another, wrong every time. So for anything about chickens that I do not already know, I try to double-check it with other sources to see if it might be correct, or if it is a new kind of wrong. I don't personally have experience with ESA chickens, so I am looking at this as how it relates to chicken needs that I already know about. For example, I am assuming that chicken diapers will be an important part of taking a chicken to places that poop on the floor would be a problem.
Overall with any kind of animal, some are more accepting of new situations than others. Yours sounds like she may be off to a good start. So I would try to keep exposing her to new situations as you can, to try to help "new" be a normal part of her life. That could include having people over to visit so she sees strangers regularly, and it could also include putting new things in the coop and run regularly, or near it. Things like a rock or log to climb on, or a handful of hay to scratch through, or a cabbage to peck, can be scary the first time a chicken sees them. Moving a strange object like a wheelbarrow or a lawn chair near the chicken run can give the whole flock exposure to another kind of new thing that doesn't actually hurt them. Re-arranging things regularly can help the chickens be used to changes, instead of expecting everything to be exactly the same every single day. You can wear different clothes from one day to another (different colors, different shapes or silhouettes.) Of course you don't want them to spend all their time scared, but don't go out of your way to avoid changes either. Some people do things the same way every time, and they sometimes end up with chickens that freak out if they wear a new hat or a different pair of boots (the opposite of what you want.)
Some of those ideas relate more to the whole flock than to this individual chicken, but having a varied environment (while still safe) shouldn't hurt any of them and might actually be good for them all, while especially being helpful for the particular chicken you want to train for extra experiences.
That part of your plan sounds good to me. I agree that exposing her to that environment would be a bad idea.
I hope you are also planning some kind of harness & leash, or a carrier for her to ride in. A scared chicken can fly away before the person has time to react, and then it can be difficult or impossible to catch the chicken.
Especially at first, I would only take her places where a chicken would be allowed anyway. For example, if a given store allows pets, take her there for the experience, not to a place that has a "no pets" policy. This gives her experience in going places (probably starting when she is a bit older) without you having to argue about her being allowed vs. not.
As she gets older and you see how things go, you will be gaining the experience to decide what other places you can or should take her.
I can see how that makes sense. When choosing an animal for a particular purpose (like ESA), I wanted to be sure you at least considered whether it was a suitable kind of animal, because some species do have a temperament that is more or less suited to certain kinds of situations. I notice you already picked the chick that was most inclined to spend time with you, instead of going off to do other things, so that's a good starting point.
Just a comment, chickens often have shorter lives than dogs do. I don't know if that will affect your plans.
I see why you figure she must be a Rhode Island Red! But if you have other Rhode Island Reds and she does look different, she might not be one. Sometimes a hatchery will add a free chick, or substitute one if they run short. Did you already figure out who the Olive Egger is?
It will probably become more obvious as she gets older, because she will either look more like typical Rhode Island Reds, or she will look even more different (hopefully in a way that answers the question!)
