The wire you want is commercial equivalent to jumper wire. In the military it is Mil-W-16878 type 1 which is a PVC based wire. What makes it so flexible is the stranding. Use 19 strand or higher. Again a good electrical supply house should have it. Also telephone jumper wire will work as long as it is stranded.

Wire companies like Judd Wire, Raychem, Brand-Rex make it for commercial and military applications.