Hi Tsubasa
Flickering tends to be caused by automatic adjustments in the camera and/or reflections from things out of shot (like the animator's white shirt) or by unsteady light sources giving out  imperceptible changes in intensity over time.  This is an inherent problem with any flourescent source because they are flickering instruments.  Full spectrum basically means pure white light, so it's main use would be as a working light - it's better on the eye. 
By all accounts full spectrum lighting may not produce spectrally balanced lighting any better than lighting that is not marketed as full spectrum. It certainly won't solve a flicker problem in animation.  Your camera's white balance and post production software will be able to adjust to make any broad spectrum light appear any colour you want anyway. 
Tungsten and halogen lighting will tend to offer a more steady source of light but of course the power consumption is much much higher.
If your camera (or capture software) has an averaging option, where the camera takes several images for each frame and incorporates data from all those images into the single frame it records, that can counteract the instability of flourescent sources. It's a function designed for reducing image noise from low resolution cameras but it has this useful byproduct.
I hope that's helpful.

Ben