The LCD is simply incapable of representing all the brightness levels and colors that would be required, not even close. The viewing angle is very limited so brightness can change just by looking at it from a slightly different angle. The HVX also lacks the required menu function such as B&W display and blue gun.
If you absolutely have to do it then follow this tutorial, it's a universal calibration method for color bars.
there are a lot of procedures (all basically the same) if you google for it. If you have to use the flip out LCD then tilt it to obtain the best visual reproduction of calibrated bars and be sure that's the view you use when shooting. An external good monitor would be much better.
The flip out monitor was never really meant to be a color reference tool. It was designed to be used for framing shots and for monitoring camera functions.
As DGW stated if you are looking for color and aperture reference- an external monitor is the way to go.