It can take up to 48h for the milk to drop and the doe feeding the kits, and then only twice a day for a few minutes - some does do not go near the nest as long as they feel being watched. It's very rare that I see one of my does nursing.
As for flipping the doe...
I put a towel on my lap, sit on a chair, kits between my legs, and put the doe on top - so I can cover her face or pet her with one hand to keep her calm and hold her with the other, keeping her hind feet well away from the kits. Mine would be totally stressed out when I would flip them, and they would kill everything in reach with their claws, they are not used to being handled much.