Flickr is one of the best online photo sharing sites but it is clumsy identifying relationships for who should have access to photos.
You need to add people to your contacts by sending them an invitation they can accept. When you send the invitation it is identified either as a friend or family by a check box. When they accept via email they will then be able to see your photos and quite possibly vice versa (reciprocal agreement). This is how it should work with a check box for confirmation since in most cases people will want reciprocal agreements. It may be (TBC) that to see their pictures they may need to add you to their contacts and identify you as family separately.
To send an invitation go to your contact list and pick someone who already has contacts you want to add. Click on that person’s profile link to see their contacts and click on one of their contacts you want to send an invitation to.