People have done this of course, but you cannot convince a flat earther with GoPro footage because of the fisheye lens that will allow you to film the horizon curve either way, depending on the angle.

What you'd need is a wide angle rectilinear lens not normally found on light weight cameras.

He shouldn't expect much from 1800 feet tough in terms of seeing the curvature. It won't be pronounced. I think he just wants to fly.