Ps do not pick the flakes or feathers as this will cause discomfort and may further infect!!
VG can cause them to have faecal matter around or on the feathers directly near their bottom, so may help to trim those feathers down to keep the mess to a minimum.
I know this is too late for your hen but perhaps may save a life in the future!
From what you said and the pictures, it sounds and looks like 'vent gleet' or something along the lines of that. Its a fungal problem similar to thrush but if left untreated will spread and eventually kill a hen.
I...