What is the difference between Refresh Rate and Flicker Rate?
In the context of a CRT vs. flat panel, that is a Cathode Ray (vacuum) Tube, you have to consider the following:

1) Video sync as broken down to Vertical and Horizontal scan rates.

2) Phosphor persistence (the length of time the phosphor coating on the inside of the CRT will glow). "Phosphors are available with persistences ranging from less than one microsecond to several seconds."

http://en.wikipedia.org/wiki/Cathode_ray_tube

These two factors will determine the overall picture quality with regard to time.

Refresh rate would be best explained as vertical frames per second, for NTSC it is 60 fps.

Flicker rate includes the refresh rate plus factoring in the persistence of the phosphor.

Long persistent phosphors were employed in radar screens and O'Scopes as to allow objects to last longer on the screen while shorter persistent phosphors were employed in most consumer TVs to reduce motion blur.

"Flicker occurs on CRTs when they are driven at a low refresh rate, allowing the brightness to drop for time intervals sufficiently long to be noticed by a human eye..."

http://en.wikipedia.org/wiki/Flicker_(screen)