I don't think there is an ASME spec for the packing. The pervasive practice in the industry is to call out the spec number from the packing manufacturer used, unless the ball  valve manufacturer just wants to keep the packing spec proprietary. 

Example: Masoneilan (I do not work for them) identifies their packing as Crane 285K.  This particular packing is a square-cross-section aramid fiber (Kevlar) skive-cut ring with a TFE overbraid.  For an all-braided TFE ring, they call out Chesterton 324.  Other packings are just called out as TFE V-ring or Grafoil.  If you look at (which is clearer than the ASTM site), and search for PTFE you find a number of standards for 'Virgin' PTFE Tube (which I summise you are using). There are also PTFE composites within the ASTM List.
 I am afraid that is as close as a standard as you will get, but at least that controls the material if not the design.

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