Flickr is a private company. Therefore, it is free to censor photos and comments, which it apparently does with pride and gusto.
Flickr is a private company, of course, so it is no subject to any legal argument regarding “free speech.” At some point, however, after tens of millions of people adopt Flickr as their photo and comment community, it does seem to function like a government. But, again, Flickr is a private company and it can do what it wants.
We have the same potential problem with many private entities that now control the flow of huge amounts of information (e.g., Google). It will be interesting to see how this situation evolves, especially to the extent that these private companies seek to distort the flow of information for private gain or for capricious exercise of power. It’s not like it hasn’t happened before–think of the mass media. But also consider the telecoms: one increasingly hot angle on this issue is net neutrality.