what year or other info on your F-4J?
forget the sheen for a moment, but, unless you are doing a very late TPS NavAir bird,,,,,,it's Light Gull Gray on top, and White on the bottom, with White on all control surfaces, top or bottom
if the date is right, you might also see your bird in overall Light Gull Gray, with White still inside of the doors and wells as before,,,,,,,,,the dates also dictate the sheen, but, I cheat and make all mine overall satin,,,,,not much point in getting some of the sheens right,,,no one has ever built a Phantom model with ALL the sheens right that I have ever seen
but, early days,,,,,,Flat Light Gull Gray topside, Gloss White underside and control surfaces, and inside wells, etc,,,,,,,later in the early seventies, Gloss top and bottom
the Gloss wore into a more Flat look with service wear,,,,and the Flat sort of "boot polished" up into a more Glossy look,,,,,,,hence my choice of Satin, that meets both in the middle
Rex
edit, just scrolled on back and saw you are building the F-4J Warlords,,,,,,,if that is the AA tail code for the Bicentennial, that time period makes it Gloss Light Gull Gray on top, and Gloss White in the white places,,,,,,,,,and I left out part of your color question,,,,,,,any photos you see of NavAir birds that appear to be "some gray" on the underside,,,,,,are either just shadowing on an early jet, or the same Light Gull Gray as the top on a late jet,,,,,,,except for the Tactical Paint Scheme jets,,,,,,,those are so tough to call that even kit makers and decal printers hardly ever agree, lol