Yep, FlashCom easy way is using Shared object. Some simple snippet to get users recordings of some song from a combobox looks like this:
//Conect to the app
var app = "rtmp:/karaoke/"+myList.getSelectedItem().data
// load a remote shared object
_root.rec_so = SharedObject.getRemote("recordings", client_nc.uri, true);
Anytime a user records a song, a reference is added to the recordings SO and then is used to retrieve the info.
Database could be integrate trough (at least) two ways: as usual not regarding to the FlashCom server and mixing the data inside the movie, or integrating the database call trough Flash Remoting, so you can use Flash Remoting calls in the ActionScript Serverside, mixing FlashCom and Flash Remoting calls.