I doubt there’s an easy ready-to-use solution if you want a full 360-degree view; if you search for “360 video” you’ll find a couple other threads like this one which has some samples but no directions on how to do it, because it required a lot of custom tooling and manual work:
For a less ambitious recording of just what you’re seeing from the VR screen, I did some experiments a while ago and wrote up some notes but I found it was not super great because the pilot’s head movements and limited field of view are forced upon the viewer: