Start with a slow slide up from the bottom white bar. The app will get smaller and you'll feel a quick vibration. You'll see the top of the next app appear below the one you're currently on. Then release your finger. That bottom app snaps up and now you're in the same mode as if you pressed the little nav square. Scroll up and down and swipe away whatever app you want killed.
Just make sure you swipe it to the outer edge of the phone to kill it. Otherwise, you swipe in towards the spine and send it to the other screen.