DisplaySearch posted an interesting flexible OLED market forecast. They say that in 2015, the market will grow almost nine-fold over 2014 - as new mobile phones and smart watches with flexible OLEDs (including Apple's Watch) hit the market.
Looking further into the future is more complicated as some of the mass-production technology isn't ready yet and demand is not clear. DisplaySearch has three different scenarios for the flexible OLED market. In their "likely" scenario, the market will grow at a CAGR of 119% from 2013 - and will reach over $20 billion in 2021.
Samsung recently announced that flexible OLED is one of its 3 areas of future growth and the company is set to release foldable OLED devices towards the end of 2015. Samsung is currently producing flexible OLEDs in a 5.5-Gen line with a capacity of only 8,000 substrates per month. A few months ago the company confirmed that it is constructing a new 6-Gen (1850x1500 mm) fab that will be dedicated to flexible OLED production.
LG is also increasing its flexible OLED production capacity, as the company sees tablets with flexible OLEDs and bendable phones arriving in 2016 and rollable devices (including rollable TVs) in 2017. LGD unveiled 18" rollable OLED prototypes earlier this year.