LG Display's CEO Han Sang-beom said that the company plans to start mass producing flexible OLED panels in the second half of 2013. He wouldn't say whether they got any orders for the next-gen flexible panels, but obviously there are speculations that Apple is behind those orders. It's probably unlikely as capacity at first isn't likely to be enough for Apple.
This actually marks an expediation of LG's flexible OLED plans. In January 2012 the company said that they will start constructing a new pilot line in Q3 2012, which will become active by the end of 2012 and the company will need 1-2 years to develop and verify the process before producing at mass volume.
LGD was also selected by the Korean government to lead a project that aims to produce 60" flexible and transparent UHD OLED panels by 2017. A few days ago we reported that Aixtron sold a 3.5-Gen flexible organic electronics production equipment, and LGD may be the company that bought the new machine.
Samsung's flexible OLED program seems to be more advanced than LGD, with plans to start mass producing panels by the end of 2012. There are some rumors that the upcoming Galaxy Note 2 phone (that will be unveiled on August 29) will sport such a panel (which Samsung will brand as a YOUM display).
LG Display's flexible OLEDs will use the same technology as Samsung's flexible prototypes - a polyimide coated substrate and direct-emission RGB sub-pixels (as opposed to LG's OLED TV which use WOLED with color filters).
Han Sang-beom also says that LG's OLED TVs will debut "very soon". The company will significantly boost its OLED TV production capacity at the second half of 2013.