Unfortunately there is no way for 3rd-party DJ style apps such as djay to play songs from Apple Music, Apple’s music streaming service. This also applies when songs are downloaded onto your device from Apple Music, as the downloaded files will be DRM-protected.
That being said, djay provides a sophisticated integration for all tracks downloaded onto your device (via iTunes). You can browse your music library by Playlist, Artist, Album, Genre, Key, History, and more.
Furthermore djay integrates with Spotify, giving you instant access to millions of tracks. Spotify integration in djay includes all of your existing playlists, starred and saved songs, powerful search capabilities, charts, browse, and Match for intelligent song recommendations.