Well, I think I can remember most of the key colors. (I'm typing at the office and don't have the Campbell plans in front of me, but I think I remember most of them.)
The hull above the waterline is black; below the waterline it's sheathed with copper (actually Muntz Metal, which is less red than pure copper - but that's getting pretty finicky.) There is not, contrary to what one sees on some models, a white stripe at the waterline. There are three wood rails, or moldings, near the top of the hull. The one at the very top (the caprail) and the one immediately below it (which divides the wood "monkey rail" from the sheet iron bulwark below it) are varnished teak. The lowest rail - the big one at the base of the bulwark, which runs all the way around the ship - is white.
The figurehead is white, with a thin gold line around the base of the witch's chemise (the "cutty sark"). The other carvings at the bow and stern are gold-leafed.
The insides of the bulwarks are painted white. The waterways - the horizontal surfaces forming the edges of the deck - are in fact iron, filled with concrete, which, somewhat surprisingly, is painted red.
The deckhouses bulkheads are varnished teak. (Late in her career the panels on them were painted white, but originally they were unpainted overall.) The decks, and the roofs of the deckhouses, are bare, unfinished teak.
The turned railing stanchions at the break of the poop deck, the pinrails, the fife rails, and most of the other deck furniture are varnished teak. The edges of the three cargo hatches are sheet iron, painted white. The hatch covers are unpainted wood.
The two little box-like structures just aft of the forecastle deck (which in fact are toilets for the crew) are painted white.
The pumps aft of the mainmast, the cargo winches, the little winches on the bulwarks, the various mooring bitts, and most of the other iron deck fittings are painted black. The wheels of the pumps are red.
The ship's boats are painted white outside; the thwarts are unpainted wood.
The lower masts, the tops, the crosstreees, and the doublings (the areas where the different components of the masts overlap) are painted white. The portions of the topmasts and topgallant masts where the yards slide up and down are unpainted, oiled wood. (The ship's website has lots of photos that should make this clear.) The bowsprit is white, as is the inboard portion of the jibboom (where it overlaps the bowsprit). The outer part of the jibboom is white.
The yards are black. The do NOT have white tips.
The spanker and spencer gaffs and the spanker boom are white. The studding sail booms are unpainted, oiled wood.
I think that covers most of it. Again, the photos on the website (those taken before the awful fire of a few years ago) should clear up any questions.
Hope that helps. Good luck.