Yes, teachers and parents can save an individual item from Seesaw to their device, share it into another app (Facebook, Twitter, Email, etc), or get the embed code for an item (for adding to a blog) by tapping the More button (three dots) below the item, and then tapping Share Item.
You can also save items to your computer from the Seesaw website. Just click the More button (three dots, the same as it appears on the app) and the item will be downloaded.
Teachers can also enable the Save to Camera Roll setting for their entire class. All items created in Seesaw will also be saved to the device camera roll when this setting is enabled. Tap Menu button > Manage Class > flip the Save to Camera Roll switch to ON.