I suspect speed would be the issue here. As you know flex shafts transmitting considerable power are possible. However these are generally used in low speed grinding applications.
On top of that the life span of these shafts is not infinet and eventually break no matter what bend radius percsustions you take. Of course everything breaks over time but i can see CNC being especially hard on the shafts. Remember the shaft has to compensate for changes in vertical as well as lateral position and frankly im not sure success can be had without a spline drive. The only other option i know of would be an extremely long shaft that would form an upside down U.
I supose you could check with Foredom or similar manufactures for design assitance. They do have fractional HP drives. My guess is that they would decline to support such application.