IHS says that flexible display shipments (mostly OLEDs) will reach 139 million units in 2017 (or 3.8% of the total display market) - an increase of 135% compared to 2016 (59 million units). In 2023 IHS sees shipments of 560 million flexible displays.
In 2017, flexible OLEDs will comprise 20% of the total OLED display market. The growth in flexible OLED adoption will be lead by smartphones - and especially Apple's next-gen iPhone. In 2016 76% of flexible OLEDs ended up in smartphones - and the remainder were used in smartwatches (mostly in Apple's Watch, probably). Next generation flexible OLED applications, including tablets, VR devices, automotive displays and OLED TVs are not expected to be significant until 2023.