Some apps don't have AirPlay support built-in, but that doesn't mean you can't force their audio stream to an AirPlay-compatible device. There's an easy way around it that only takes a few extra taps.
All you have to do is start playing a song (or whatever), lock your phone, tap the home button to bring up the home screen, tap it two more times to bring up the iPod controls, and then you'll see an AirPlay button. Just tap that and you'll be able to select the device you want to stream to. If you want to switch it back you'll have to do it from the lock screen as well (or from another AirPlay-compatible app), but that's not a big deal to enjoy streaming your audio even when an app doesn't support it.
For a demo, check out the video above.