SoundCloud integration in Amazing Slow Downer lets you playback songs from all of your existing SoundCloud playlists and the songs you have in your "Liked Tracks" list.
If you miss a song, just switch over to the SoundCloud player app and add the song to the "Liked Tracks" list or one of your playlists.

The button top right looking like a circle with an arrow is a "Refresh" button. Tap on this in case of network problems.

You need a "SoundCloud Go+" subscription.