Hi there, here’s how it works for reblogging flickr images:
The people on flickr can choose whether to make their images Private (so they can’t be shared) or Public (allowing them to be shared). When they are Public the small links above the images (like Facebook, Twitter etc) will light up; if they’re private, they’re dull and can’t be clicked.
In my accounts I’ve arranged it so Tumblr (linking to my blog) will show up along with the other buttons. When I click the link on an image I like (if it’s lit up), it’ll go to my queue with the credit links and source.
So since the images are on Public, and as long as I keep the links/credits/source and don’t claim them as my own, then making them shareable was decided and deemed fine by the owners.
If any of the photographers were to ask me to remove an image, I would do so (I would also mention maybe changing the privacy settings if they haven’t already done so to save further mix ups).
If in doubt, you can always check their profile so see if they have any disclaimers posted, or to send them an email.
Hope this answers your question :)