How to Block Photo Downloading on Facebook
Block nonfriends -- and certain individuals you have designated as friends -- from downloading your photos on Facebook by making the photos unavailable to them in the first place. It isn't possible to remove the download link from the bottom left corner of photos you post to Facebook. As a result, the only way you can prevent people from downloading photos from your Facebook account is by making the photos unavailable to them entirely.
Select "Privacy Settings" from the "Settings" drop-down menu after logging in to your Facebook account. Select "Customize Settings" from the "Sharing on Facebook" pane.
Choose the drop-down menu next to "Posts By Me." Select "Friends Only" to prevent nonfriends from viewing -- and therefore downloading -- photos.
Select "Customize" to block specific friends from viewing or downloading your photos. Input a friend's name, click his profile picture when it appears and then choose "Save Settings."