When Apple adopted a flexible OLED for the Watch, it immediately sparked the discussions of whether - and when - they will finally adopt an OLED display for the iPhone.
Apple is set to unveil the iPhone 6S next month (on September 9) - and new rumors suggest that it will use motion-wallpapers for the lock screen, like the ones used in Apple's Watch. Some see it as a sign that the new iPhone will also use an OLED display.
Apple iPhone OLED rumors never die. The time will come for Apple to adopt an OLED for their most popular device, but I do not think it will come in next month's new device. OLED production it still dominated by Samsung, which means that there is only one supplier (which Apple will not accept for the iPhone) and even Samsung's own capacity will not be enough to satisfy Apple.
I would guess that the earliest year for a possible OLED iPhone is 2016. Some estimate that it won't happen before 2018.