Flox is easily integrated with the facebook API.

The usual way to go about this is letting your players log in with their facebook account and then bind their game data to this account using Flox. Start out by using the code snippet below:

//Fetch the player's facebook ID
var id:String = "john-doe-123";

//Hash the ID to ensure player privacy
var hash:String = createUID(16, "facebook-" + id);

//Authenticate the player with Flox
    function onComplete(player:Player) {
        //Yay! The player is logged in!
    function onError(message:String) {
        //Darn! Something went wrong while authenticating the player.

There’s more documentation on identifying players with Flox over here.