Most of us would love to have a concrete floor for our coops-unless you live in an low-lying area where water tends to collect. Concrete does not do well in damp areas and one must modify the design to allow for drainage. In some cases chickens will use the concrete as a source of grit and eat the material. Doesn't seem to bother them.
My Father-in-law had concrete in his chicken coops and his design allowed him to simply use a hose to spray the debris. He did not do this very often as the coops were located in the shaded area and the cement took some time to dry. In his case he could have used more ventilation to help dry the floor and prevent mold growth.
You mentioned your chicken had problems with her feet. This could be bumble foot which should respond to daily application of diluted iodine solution(warm solution works best) for a week or so. If you are dealing with scaley leg mites you'll have to not only treat the chicken but treat the area she stays in. With scaley leg mites I've had success with washing the entire chicken with a cat flea shampoo-making sure to soak the feet-rinse very well and dry the chicken. Apply a thin layer of Vics Vapor ointment to the feet and legs once a day for a week, stop for a week, and apply the ointment again for a week. During the three week treatment wash the chicken once a week, rinse well, and dry her. Remember to use a THIN layer of ointment as too much can retain moisture and prevent healing. Severe cases of infection will require oral antibiotics.
Treat your coop by throughly saturating the surfaces with permerthrin based barn spray. (Remove all chickens from treated area until dry-use fans to improve ventilation if needed. If the hen is in your house be sure to clean the area thoroughly everyday-including the material exposed to her. If you are using towels wash them in the hottest water possible (you can use the cat shampoo for this). If you are using shavings you'll have to dispose of them on a daily basis. This will help break the life cycle of hatching eggs, pupae and so forth.
Good luck and keep up the good work!