It seems from the Nikon papers that the SB-800 is compatible with the Z6iii, when mounted on the camera.
[URL unfurl="true"]https://onlinemanual.nikonimglib.com/z6III/en/compatible_flash_units_379.html#sub_sb-910_sb-900_sb-800[/URL]
I currently have the Z6 (i) and it works fine. I will get a Z6iii within a week or two, and can then give more accurate answers.
