Check out the link in my signature for my thoughts on space. A lot of those won’t apply to you but some will.
I have no good way to attach to vinyl without damaging it. If you are going to use that space, I’d be real tempted to just close off the open side and use the walls of the house as the walls for the run. Part of that is resale value of the house but if you close off any small area you or the chickens can’t get to, you create a great place for mice to set up housekeeping. The chicken feed will attract them. Mice can attract snakes. I really don’t like to set up spots that attractive to mice, especially right around the house.
There are other potential problems having the coop and run that close to the house. Hens are not nearly as loud as roosters and they should be pretty quiet at night, but the noise may possibly bother you. Many of us enjoy those sounds but the egg song or other sounds they make can be surprisingly loud.
Chicken create a lot of dust. They are always scratching. That dust can be dried dirt, dander, dried poop, disintegrated bedding, about anything dry. You might not want to open that kitchen window because of the dust. Hopefully no one is allergic to chickens?
Another potential problem is smell. Smell normally comes from wet or damp poop. If you can keep everything dry and prevent the poop from building up, you can pretty much eliminate smell, but that is not always easy. You can set up a droppings board in the coop under the roosts to catch and eliminate the poop they deposit on the roosts at night, which will help reduce the poop you are dealing with, but you still need to control moisture. You’ll have enough poop in the run that if it gets wet, you’ll have smell.
There are two basic principles to keep things dry. Don’t let water in to start with. Cover the run and slope the roof of the coop and run so water flows away. Snow and rain can blow in from the sides, not just from straight above. Use guttering and downspouts to get water away from that area. I see that downspout in your photo. You might need to pipe that further from your house. Don’t locate your coop and run where rainwater runs into it when it rains.
The other principle is to get any water out that manages to get in. Good ventilation will help things dry out and keep smells from building up. Your run floor needs to have a place to drain to and needs to be a material that will actually drain. Clay holds water and the chickens will dig holes in it when they take dust baths that turn into mud puddles when it rains. Sand drains really well as long as the water has a place to go. That means it has to be higher than the surrounding area. I’d give a whole lot of thought to filling that area with several inches of sand and maybe using French drains to get the water away from there.
As far as not spending a lot of money, check out Craigslist for people giving away or selling stuff cheap, maybe even buildings you can relocate or tear down for the materials. Go dumpster diving or drive around on trash day for things you can use. You probably have one of those “recycle” places where they sell recycled building materials pretty cheaply. Maybe you can get a door or window for next to nothing. You’re also looking for hardware as well as lumber or wire.
Personally I would not use that area because of the potential for smell. I think it is going to be really difficult to build something you can keep dry enough without attaching to the vinyl. I wish you luck!
