5 girls and 2 boys would probably work fine, provided the drakes are not too over-enthusiastic with the ducks in breeding season. You could start with that number and see how you go.
Ducks explore the world with their mouths. They love to nibble at things. In the wild they'd be exploring and nibbling all day long. Also, pin feathers are tasty and made of protein and blood. If the ducks don;t have anything else to explore with their bills then they will start nibbling their sibling's feathers and suddenly you have a feather picking problem. So in addition to what you have done already I'd:
- Have a look at the size of the brooder/pen you have them in. Is it big enough so that they are not overcrowded? Not sure how old your birds are but at 4 weeks you can fit about 6 per 10 square feet. At 6 weeks only 4 per 10 square feet. After 3 weeks they should have access to a bigger (predator proof) outdoor area during warm days. I got those figures from Holderread's books.
- Do they have enough interesting stuff in their environment to entertain them? Bedding that they can snuffle around in? Mushed up peas and chopped greens to nibble? Regular supervised swimming time so they get exercise and are not bored? Try hanging a few bird toys or cat toys in their pen/brooder for them to play with.
- Do they have food that is suitable for ducklings their age, to make sure they are getting the nutrients they need?
You can separate the Khaki if the other things don't work but rather than taking him/her right away (which will be distressing for the duckling) maybe just section off a little area with wire mesh (with separate food and water) so they can still interact but not eat the others' feathers.
I hope that is useful and that you can solve the problem. It sounds like you have got onto it fast so good job there