It’s sort of confusing since sometimes it’s used as a synonym for skin, and sometimes it’s used to mean somebody’s insides. Generally it would not mean organs or bones, though.
Do you think flesh = soft tissue and is a collective term for skin, muscle, fat and anything else that’s not bone or an internal organ?
Either muscle specifically, or all soft tissue in general, depending on the context. “Only a flesh wound” means that it was only muscle, not any organs, so it’s not life-threatening.
Or, of course, it can metaphorically be uncovered skin.
I’m sure you could make a very clever wordplay/joke in some poem or book or whatever by intimating that someone does “not eat the flesh”, but shows them chowing down on gallbladders or sucking bone marrow.
However, it would be clever because it’s subverting expectations that “not eating the flesh” tends to imply not eating other parts either. I’d call it a bit of synecdoche, but it’s definitely aided by the fact that “flesh” is a pretty fuzzy term to begin with.