I'd want a walk-in coop for more than 8 chickens. Yeah, that pretty much limits a lean-in coop to 4' x 8'. One of the big mistakes people make is to try to squeeze too many chickens into too little space. I find the more I crowd them the more behavior problems I have, the harder I have to work, and the less flexibility I have to deal with issues that come up.
Chickens do not have a concept of coop space versus run space. All they care about is having enough room when they need it. If you build it so the run and coop are predator proof and you never close the pop door so they have all that run space available you can get by with less coop space. In certain circumstances that can work.
But in Kentucky there can be a problem with that. In winter when you get snow, ice, and cold winds the outside space is not always available. They can easily be stuck in that small space for a few days, that's when you can really have behavioral problems. Problems like fighting, feather picking, and cannibalism.
I like to build in dimensions of 4' and 8'. Most standard (less expensive) building materials come in those dimensions. 8 feet2x4's. 4x8 plywood. If you use those dimensions you have less waste. So, yes, I like the dimensions you are mentioning. 8x8, 8x16, 8x20. Even the 4x8 but that is not going to be big enough with that design.
For 15 hens you will probably want 4 nests a minimum of 12" x 12" each. You don't have to have 12" of roost space for each bird, with 15 hens they can roost closer than that, but you don't want to squeeze the too tightly. In an 8' building I'd want two 8' long roosts. It's efficient. Two 6' long roosts would probably work. By the time you add food and water in there you quickly have a need for more space. You don't want them pooping in the food, water or nests from the roosts.
I strongly urge you to make the enclosed "coop" portion a walk-in maybe 8x8 or 6x10 if not larger. I know, 10' is not divisible by 8' or 4' but the cut-offs can probably be used for nests or something else. That way you can leave the run open with wire mesh. You can try covering the run and walling it in to keep out snow and a cold wind and go with a smaller coop section, but that could wind up more expensive and harder to clean and maintain. I think it will work a lot better if you don't try to squeeze it down too much. If you are aggravated from working harder than you need to you probably won't do a good job and will not enjoy it.
