Here’s the example files for
https://www.permadi.com/blog/2011/02/using-facebook-graph-api-in-flash-as3-to-post-to-photo-album/:
/tutorial/as3-save-photo-to-facebook-album/as3-save-photo-to-facebook-album.zip

Remember to change the APP_ID with your own APP_ID in order to make it work on your server domain (i.e.: the APP_ID in the FLA and client_id in the index.php).  You can rename the index.php to index.html if you are not using php.
The example is written in Flash CS3, but should be easily ported to Flex and should work in CS4 and 5.

The above download already contains the facebook-actionscript-api, but you can download their latest at  http://code.google.com/p/facebook-actionscript-api/downloads/list

IMPORTANT UPDATE NOTES

Due to changes on Facebook API, these elements must be changed:

• response.session should be changed to response.authResponse.
• perms is now called scope.

The source link above has the changes already implemented (there are changes in the Javascript and AS side). Do directory comparison using something like WinMerge to see all the changes.