We demonstrate large area fully flexible blue LEDs based on core/shell InGaN/GaN nanowires grown by MOCVD. The fabrication relies on polymer encapsulation, nanowire lift-off and contacting using silver nanowire transparent electrodes. The LEDs exhibit rectifying behavior with a light-up voltage around 3 V. The devices show no electroluminescence degradation neither under multiple bending down to 3 mm curvature radius nor in time for more than one month storage in ambient conditions without any protecting encapsulation. Fully transparent flexible LEDs with high optical transmittance are also fabricated. Finally, a two-color flexible LED emitting in the green and blue spectral ranges is demonstrated combining two layers of InGaN/GaN nanowires with different In contents.