Engadget said they got hold of the following "press renders" showing LG's upcoming LG G Flex phone that will sport a flexible OLED display. Engadget also reports that they confirmed that the OLED panel will be 6" in size and the phone will be announced in November.
As you see this phone is curved from top to bottom. I think this makes more sense than Samsung's Galaxy Round which also uses a flexible OLED but is curved from left to right. Of course we'll have to wait for someone to review both phones to see which design is better. I'm guessing in coming months we'll see several new phone designs using flexible panels as makers try to figure out how best to use curved displays.
Earlier this month LGD announced today that it will start mass producing flexible OLEDs for smartphones. The first panel is indeed 6" in size. It weighs just 7.2 grams and is only 0.44 mm thin. LG Display has a flexible OLED 4.5-Gen pilot line that has a capacity of 12,000 monthly sheets, which translates to probably around 200,000 to 300,000 monthly 6" panels (depends on the production yield).