If the screens you're filming are LCD's, you don't need to worry as modern LCD's maintain their image unless it is changed - no flickering.
If those are CRT's, then you need the shutter speed of the camera to be slower than or at least equal to the refresh time of the CRT. Example
(shutter speed in 1/s on lower right corner, CRT is an US-freq device).
Common CRT refresh times are 1/60th of a second for US NTSC systems, and 1/50th for European PAL systems. But as these were fixed according to mains power frequency, and on aircraft this usually is 400Hz I have no idea how they do it on aircraft screens. If I had to hazard a guess I'd say they would have kept the 50/60Hz.
Back to the filming part - if your camera has a fully manual mode where you can fix the shutter speed yourself then simply dial one that is slow enough to incorporate a full screen refresh. If not, it should usually have some kind of "exposure control" instead, which we don't really know what does - but if you switch to manual and change a couple of steps up/down you should be able to find a spot where flicker is minimal, and you can leave it there. That's how I did on these 2 videos:http://www.flightlevel350.com/Aircraft_Air...ideo-11290.htmlhttp://www.flightlevel350.com/Aircraft_Air...ideo-11291.html
as the small camera I used for those doesn't have full manual control.
In auto mode cameras usually try to stay as close as possible to the 1/50-1/60th shutter speed to recreate typical motion blur, whether they can stay there or not depends on illumination, what aperture range the lens has, whether an ND filter is available...