As the IT person in my company, I could use Flickr instead of a website photo gallery. It might free some download space on the host server.....
In the classroom, I would use it after a field trip to display images of what we saw. Then, the students might write a brief summary of a particular picture and what they learned.
I would also use it as assignments, such as, "Find and take pictures of examples of things that are symmetrical." After they upload their photos, we create the collection on Flickr for all to view the real-life examples.
I would use Flickr as a spring board for ideas. I can see showing photos to stimulate creative responses or ideas for writing stories. Sometimes just a photo is enough to spark that creative process.