Goats can be like horses and need a good grooming. I would use food grade DE and rub it into their coats then brush them out. We do it in the summer time and it keeps the flies at bay too. In winter our goats have such thick coats they look like they have been at the furriers. lol
The flakiness could be lice.. could try the DE rubbing it in and giving them a good grooming and/or a oral dose of ivomec injectible.. would clear up any buggies..my goats loved to be brushed, more so than my dog!! and right now they are starting to lose their undercoat fluff and look really scruffy.. plus finding clumps of goat fluff on fence, gates, barn walls, my pants, etc.. wherever they rub.. My bucks are really greasy and gross but they are intact and seemingly pee on themself any chance they get.. and with the combo of loose mineral and natural dust from barn they are GROSS! Cant wait till warmer weather where they will get out in fresh air and sun!!!