Where do you live? In states likes Florida, stick tight fleas can be a problem, but mites or lice could be a problem. The stick tight fleas are larger. You can use permethrin 5-10% spray or poultry dust to treat all of those. If you Google any of those pests, you can find pictures to identify them. You may also do a search here on BYC at the top of this page (search forums) for more threads.
After rereading your first post, the spots are probably either peck marks from another chicken, insect bites, or if they are more brown than black, it could be fowl pox. Pox starts out with beige to tan spots, changing to brown or dark brown. Jet black spots are usually peck marks or fly bites. We always can help more if there are pictures posted.