How were silver and gold separated using the salt cementation process?
This is an old process

M. Berthelot gives it from Papyrus V from the Leyden Papyrus X, in his Introduction à l'étude de le Chimie, des anciens et du moyen âge (Introduction to the study of Chemistry, of forefathers and the middle age).
The papyrus is at least from the III° century, the process very probably older. From page 14 (my translation):


  "Take piquant vinegar, thicken, take some [lacuna], 8 drachmas of common salt, 2 drachmas of lamellar alum (schist), 4 drachmas of litharge, crush with vinegar for 3 days, separate by decantation and employ. Then add to the vinegar 1 drachma of copperas, half an obole(1) of [lacuna], 3 oboles of chalcite(2), one and a half oboles of sory(3), one silique(4) of common salt, two siliques of Cappadoce salt(5). Make a lamella having two quarters (of an obole?) Submit it to the acion of fire... until the lamella breaks, then take the pieces and view them as refined gold.
  
  
  1 drachma = 6 oboles 
  copper ore, such as pyrite
  product of alteration of pyrite, which can include both copper sulfate and basic iron sulfate.
  silique = third of an obole, a measure of weight
  a variety of rock salt"
  




What about the chemistry?

Berthelot cites the process of départ par cémentation (departure by cemetation) from Macquer's Dictionnaire de la Chimie (1778). From the latter, page 312 (still my translation):


  "First prepare a cement composed of 4 parts crushed bricks passed on a sieve, one part green vitriol calcined to red, and one part common salt: mixe the whole very-exactly, and make a firm paste, moistening it with a little water or urine. This cement is called cément royal, because it is used to purify gold, which chemists view as the king of metals.
  
  On the other hand, reduce the gold one wishes to prepare, to lamellas about as thin as billon pieces: at the bottom of a crucible or cementation pot, place a layer of the cement of thickness the width of a finger: stratify the gold lamellas on this layer: place on top a new layer of cement: thus fill the pot, always placing the gold between two layers of cement; and cover it with a lid sealed with sand and clay. Place the pot in a furnace or oven ; heat progressively, until the pot is a dull red ; maintain this level of heat for about twenty four hours: it is very-essential that the heat not be able to melt the gold. After that, let the pot cool down, and open it to remove the gold, which must be separated thouroughly from the surrounding cement: it also has to be boiled in large quantities pure water several times. One can try this gold on a touchstone or otherwise ; and if it is found insufficiently pure, submit it a second time to the process.
  
  The vitriolic acid of the brick and of the calcined vitriol, releases the acid from the common salt during this cementation ; and this last one dissolves the silver alloyed to the gold, and seperates it by this mean.


Berthelot has this to say about the chemistry occuring here, (page 16):


  By proceeding thus, the silver and other metals dissolve in the sodium chloride, with the help of the oxidative -- and then chlorinating -- action exerted by the iron oxide derived from the vitriol ; while the gold remains unchanged.


And elsewhere (page 15):


  [...] At a stretch, it could be that sodium chloride, in the presence of basic salts of [ferric oxide] [...], releases chlorine [...].


So what I think happens is: the silver reacts with $\ce{Cl2}$ and maybe $\ce{FeCl2}$ (speculation?, b.p.= 1023°C, vapor pressure at 800°C = 0.1bar) to give $\ce{AgCl}$. Then the $\ce{AgCl}$ evaporates (b.p.= 1547°C, vapor pressure at 800°C = 0.1mbar), condensates on the cement, and dissolves in it. It is unclear whether the silver stays in oxidized form. I would bet yes, but I am no inorganic chemist.



Recovering the silver

Macquer also says (page 313):


  We can see it is essential to wash thouroughly the gold, after the process is completed, to remove all the disolved silver parts, which would otherwise stay mixed with it.
  
  Concerning this silver, it can subsequently be separated from the cement, by heating it with a sufficient quantity of lead and litharge, and taking the resulting silver containing lead slag and cupelating it to remove the lead."


So apparently you can redissolve the silver in lead, and then remove the lead by normal cupellation.



Food for (even more) thought

Macquer (page 313) also mentions that the process works just as well if you replace common salt by saltpeter. Which is weird because $\ce{AgNO3}$ decomposes at 440°C.

He then adds that you can add both common salt and saltpeter, and not only does the silver still get dissolved, the gold doesn't. Which is also weird because you have all the components of aqua regia, but it doesn't attack the gold. Macquer does acknowledge his low confidence in his sources for this last process.