I actually already had a Flickr account, but I haven't done anything with it for awhile because I haven't organized my pictures. I hadn't added tags to my previously-uploaded photos. I also hadn't paid attention to the public-versus-private option.
In the school setting, pictures taken by teachers or students could be uploaded to Flickr to share. It could be photos from a field trip, an event at school, a classroom activity, or anything. If students' are in the photos, the setting will need to be private for the safety of the children. Flickr also has nice products teachers could buy. A teacher could organize the class pictures into a book to be printed and kept as a memento.
In searching Flickr, students could use the public domain photos for their own projects. It would be important to discuss with the students which photos they are allowed to use. The Library of Congress photos aren't nearly as exciting as the vast quantity of amazing photos on Flickr. So, students will need to be well-versed in the copyright guidelines. Art teachers could use Flickr to look at artistic photos with a class and discuss them.