LG Display unveiled a 5" plastic-based bendable flexible AMOLED panel at SID 2013. LG did not release any technical details. As far as we know this panel uses polyimide coated substrate and direct-emission RGB sub-pixels (as opposed to LG's OLED TV which use an WRGB technology - white OLEDs with color filters).
Earlier this month LG Electronics reiterated their plans to release a phone with a plastic based OLEDs by the end of 2013, and it seems that at SID the LG Display officials say this is still on track. LG Display is currently using their 4.5-Gen OLED fab in Paju to work on these flexible displays, which won't provide them with a a lot of capacity. LG Display may covert its 6.5-Gen LTPS line in Gumi to flexible OLED production, but that hasn't been decided yet.
According to Engadget this panel is "at least" Full-HD in resolution (1920x1080). It may sports a smaller display, and interestingly Engadget says that that upcoming phone will still come with a glass cover. I'm not sure why this is necessary, maybe we'll hear more from LGD soon.