Same exact issue here. I recently bought an iPhone 5s and I experience this sudden transition effects "gone" once every 4 or 5 days. Its like all the screens you want to get in to front comes without any effects. And yes, when you put it to sleep you can notice a little flash before the screen turns off.
My 5s came with 9.0.2, so its not an iPhone that I had to put many updates on it. I experienced ths either in 9.2 and 9.2.1. Didn't have the chance to test it under 9.0.2 since I updated it to 9.2 instantly. Pretty weird it hasn't been fixed yet. But you can be sure its not a '6' issue only.
As I said, it happens like once every 4 or 5 days. And I noticed it tends to start to happen when you turn on/off 'important' settings as turning off/on spotligh search, or certain background app refresh. Maybe its coincidence, dunno.
I feel relieved its not only an issue i have, as my iPhone 5s is new and this was driving me nutts since the beggining.