App for playing multiple tracks from different sources simultaneously
Audio playback is handled as a background task in iOS. Only one app is allowed to playback background audio in iOS at a time.

Music playing apps usually programmed to continue playback even when in background (i.e. while you are using some other app, such as Safari). As you are looking to play music via two different apps, it will not be possible if both of them are programmed to support background audio playback mode.

However, when one of the apps plays back music while not supporting background mode (such as a game app), it will be possible to playback music simultaneously from two apps, i.e. one supporting playback in background while the other is frontmost.