Tin,
You can abbreviate that code, slightly, like:
$likes = JFBCFactory::provider('facebook')->api("/me/likes");That's the recommended way in JFBConnect v5.2+ as the older getInstance method will be removed at some point.
Beyond that, you need to make sure you are requesting the user_likes permission from your users to be able to fetch their Likes. JFBConnect won't request that scope by default. You'll need to add it in the Configuration -> Facebook area for extra permissions to request from all users.
I hope that helps,
Alex