The secret to building an inexpensive flexible computer display is not in the core components of the displays themselves. It's in the material those components are mounted on.
The fundamental elements of e-ink and OLED displays are small enough that they won't break if laid down on flexible backing. The problem, according to Janglin Chen of Taiwanese government-funded research lab ITRI, is the backing itself. The substrate the components are mounted onto has to have certain physical properties, especially during the manufacturing process. To date, the primary material on which displays have been layered has been glass, which meets the needs: it's rigid, transparent, and reliable.