We are sorry to say that any flexible, including WillowFlex, won´t work with any kind of Bowden-Extruder.
Most deltabots (also called rostock, kossel,... ) use the Bowden system because they need an extremely light printhead. Also Leapfrog, Ultimaker and some others are equipped with a Bowden extruder.
A Bowden extruder pushes the filament threw a long PTFE tube (teflon) towards the extruder. Because the material is flexible, it compresses and does not give the pressure to the print head, where it is needed. It tends to crumbles and move out of the way and not into the tube.