I have a bunch of Flickr albums I use Lightroom builtin Flickr plugin publish too. Some Public some Private albums. Private with the kids.
When I upload a new photo to an already existing Private album - LR makes the entire album public and all its photos public. Found out the hard way tonight - got a Flickr email saying someone Favorited a picture of mine - a photo of 11 year old niece I uploaded today! I just went to Flickr in Safari - deleted cookies so I wasn't logged into Flickr and yup, a Private album with that new photo is now all Public. In Flickr I reset it to Private.
LR doesn't seem to respect the Permissions settings of an Album. Or at least I can't find in LR.