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In order to prevent people from downloading your Flickr photos, you can adjust the privacy settings for your Flickr account so that only people you have designated as 'friends and 'family' can see your pictures posted there. Here's how you can designate people as friends and family.
When you are logged into the site, you can designate your Flickr contacts as friends and family by going to the People menu at the top of the page and choosing List. You can also send 'Guest Passes' to people who do not have their own Flickr accounts but would still like to see your posted photos.
Marking someone you follow as a "friend" or as "family" lets you easily share with just that group of people, instead of everyone.