Flickr Lite would let me specify my name or my email. It didn't recognize either of them and it didn't ask for a password... I thought: how can it possibly log me in if it only asks for my name without my password... I also tried the names of other Flickr users but also no success. Not a good start and I am not even tempted to try the paid version if this one doesn't seem to do anything other than show public recent photos...
I have a post on my blog about common issue with this app. What's most likely happening is that you need to change the permissions in your Flickr account so that third-party apps can interact with your account.
Please reference the following blog post for common issues: http://michaelmosher.wordpress.com/2010/10/13/flickr-droid-2-4-0/
Once you allow third-party apps to interact with your Flickr account, it should be able to find your username or email address (I show you how to find your username in your Flickr account settings in the same post).
The app doesn't need a password to login; it doesn't use that kind of authentication. When it finds your username / email address, it forwards you to the Flickr website with what's called a Frob. It tells Flickr that this app wants to request access to your account, and you have to explicitly approve it on Flickr's website. Once you approve it, this app holds a token from Flickr so that this app and Flickr can mutually authenticate each other every time you use it.
Please let me know if you have any more issues with the app. It's been downloaded around 20,000 times in the Android Market with few unknown issues (most of the common problems are in the above post). I want to make sure the app works well for everyone, so feel free to contact me with questions, comments, problems, etc.
Your solution worked perfectly for me.
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