flickr authentication doesn't seem to be working or is not being saved. I tried it several times but after authenticating and getting back to instagram.app it doesn't show the toggle buttons for flickr. it's also not just me - saw some others report about this bug on twitter as well
We found a problem with devices without backgrounding when doing Flickr authentication, which we just fixed and will be submitting to Apple soon, so our next update will let you properly authenticate with Flickr. Sorry for the trouble!
This is a bug in version 1.0 that has been fixed in the latest release of Instagram. Please go to the App Store and update your app to version 1.0.2. The new version has a new icon, so you should be able to tell right away whether you're seeing the latest version in the App Store.