Picture-in-Picture is a new feature released by Apple with iOS 9; however, it only works on the iPad. Presumably, the new iOS 9 jailbreak from Pangu made it possible to get the feature working on the iPhone.
We'll let you know if a tweak is released to bring this feature to your device. Please follow iClarified on Twitter, Facebook, Google+, or RSS for updates.
You can find instructions on how to jailbreak your device here.