Weight Reducing Design Change for Extruder Driver
Very cool idea, 

One motor would definitely be more than capable of producing the required torques even through a flexshaft connector. For any normal sized 3D-printer the torques required, and the speeds you'll need for rapid response are well within the capabilities of any off-the-shelf stepper motor. 

Just a note on the idea though, with a normal, 'rigid', connection there is essentially no winding or unwinding, and only the backlash between the gears and the filament to consider, and that is effectively zero. With a flex-shaft though, the stack-up of twists and flexing will be much greater. The system will require more rotations at the source to effect the same amount of torque at the end effector as the flex shaft flexes and bends under the load. For tiny torques with short flex shafts, this wont be an issue as filament pressure is pretty minimal. But if you scale up this project or start working at much higher speeds, you may run into some issues with this design. 

I have no idea how big or fast you'd need to be working at for this to begin to become a problem. I'm imagining pretty big though. Just something you might want to keep in mind if you try turning this into a huge, super fast 3D-printer.