My bone cleaveth to my skin and to my flesh

Something funny going on here. I would take the flesh to be the meat, the part between the skin and the bones, and, to include it in this list is but to state the normal condition. Unless, that is, it's the other cleave we're talking here, in which case, shouldn't it be My bone cleaveth from my skin and from my flesh?

Edit: Man, ya proof and ya proof and then ya end up saying flesh when ya mean bones. I corrected it.