I've seen WC's come in like this. These look like maybe two different things. The black spots loo like wounds - bites or scratches. Was he in with another cham? The skin "flakes" look to me like a fungal infection (or could be bacterial) from unshed skin being allowed to stay on the cham. If this is, in fact, what it is (and it is a bit hard to tell from the pics), I have used a betaine swab and then rinsed with saline (just the CVS brand in the squirt bottle). It rinses all the betadine off and moisturizes to allow the dried ick to separate.
I also see some yellow crusty stuff at the inside elbow on the right front leg. Yellow crusty is how skin abscesses scab over. I think, based on what looks like multiple things going on, you need to disinfect the skin lesions, give a good saline wash, and get him to a vet for antibiotics or other medication. The eye is not looking good either and a nice saline wash might at least make him feel better.
Let us know how he does.