If the accessible paint is shedding off so easily, I'd start by removing the texture. Obviously, it is not adhered well to whatever is under it(sheetrock or plaster) Take a putty knife or scrapper and try removing it. Dampen any resistant areas with a spray bottle or sponge. When all is removed and dry, sand the wall and paint. It may be a little messy, but I think the weight of the skim coat is going to pull the loose texture off the wall.