How would a pilot apply the information found on a 500 Millibar Vorticity chart to a flight?
My understanding is that it shows the Isobars of atmospheric pressure at around the 18000 foot MSL altitude. It will show pressure gradients, low pressure and high pressure zones of the atmosphere at the altitude that demarcates where 50% of the atmosphere resides below. It’s main purpose is to indicate horizontal and vertical spin of air mass movement due to ridges and troughs of atmospheric pressure, wind shear, and the corialis force. This gives a good indication of the upward movement of rising air, energy being infested by a thunderstorm, and how much of spinning force is being applied to a storm to increase its risk of growing to dangerous levels. 

Typically, other aviation weather tools would point a pilot to a no-go flight decision way before reaching this one. Some pilots may use it for limited applications (like glider pilots using the skew-t/log-p diagram). This chart can be a useful tool for meteorologists and meteorology enthusiasts to come up with reports of broader scope. You will see it mentioned in Area Forecast Discussions.