You can find the official documentation for the Flickr API here:
http://www.flickr.com/services/api/
As you get familiar with the API, I recommend consulting or lurking in two communities:
The Flickr API mailing list (http://tech.groups.yahoo.com/group/yws-flickr/)
The Flickr API group on Flickr (http://www.flickr.com/groups/api/)
You can get a feel for what people are thinking about in terms of the API and get your questions answered too. When you become more proficient with the API, you can start answering other people’s questions. (The first group is more technically oriented, and the second one is more focused on the workflow of Flickr.)
API providers, including Flickr, require assent to terms of service (ToS, also known as terms of use) for access to the API. The terms of use for the Flickr API are at the following location:
http://www.flickr.com/services/api/tos/
There is, of course, no substitute for reading the ToS carefully for yourself. Here I list a few highlights of the ToS, including what it tells you about Flickr and how you might find similar issues raised in the ToS of other web APIs. Here are some factors:
Commercial vs. noncommercial use: You need to apply for special permission to use the Flickr API for commercial purposes.
Payment for use: The Flickr API is free for noncommercial use, like many web APIs are.
Rate limits: The ToS states that you can’t use an “unreasonable amount of bandwidth.”
Compliance with the user-facing website ToS: Programmatic access to Flickr content must comply with all the terms that govern human users of Flickr. This includes, for instance, the requirement to link to Flickr when embedding Flickr-hosted photos.
Content ownership: You need to pay attention to the ownership of photos, including any Creative Commons licenses attached to the photos.
Caching: You are supposed to cache Flickr photos for only a “reasonable” period of time to provide your Flickr service.
Privacy policies: Your applications are supposed to respect (and by proxy enforce) Flickr’s privacy policy and the photo owner’s settings. You are supposed to have a clearly articulated privacy policy of your own for the photos you access through the Flickr API.