Mike,
Thanks for serving our country when we need it. For what it's worth, I'm a centurion (100 landings) on the Independence. I got most of those traps in the Med. It was a few years ago, as the Indy is now a west-coast ship, I think. (Okay, okay. It was more than a few years ago. It was 1977. )
The friction modifier is used to make the differential oil more slippery. It is required only in limited-slip differentials like yours.
Synthetic oils are already more slippery than petroleum oils, so in some trucks the friction modifier isn't required if a synthetic is used. This seems to be variable from truck to truck. My truck has Amsoil 75W-90 oil, and doesn't require the modifier, but I have read of other owners who had to put it into their rear-ends (maybe "differential" would be a better word) to prevent chatter.
The way you know whether or not you will need it is to drive the truck in tight turns. If the differential oil is not slippery enough, the rear tires will skid and slip excessively, indicating that the differential is "locking up" and preventing the wheels from turning at different speeds. If this happens, you will need to add friction modifier to make the oil more slippery. You are the one who will determine whether the skidding and slipping is "excessive" or not.
If the tires do not skid or slip at all, the differential oil may be a bit too slippery already. No friction modifier is necessary, and your limited-slip differential may not prevent tire slippage as well as it was designed to do. The only cure for this is to change the differential oil to one that is less slippery.
There is a standard amount of friction modifier that is recommended for the differential, but since each truck seems to be different in this regard, most experienced people recommend trial and error for determining how much you need.
If friction modifier is required, add just one bottle to the differential. Drive the truck for a while to mix it in. Many drivers recommend driving a few figure-eights to lubricate the clutches. Then see how the differential behaves in tight turns. Again, you will determine if the tire slippage is enough or excessive. If the tires still slip and skid too much for you, add another half bottle of modifier and do the whole thing all over again. Keep this up until you are happy with the result.
The friction modifier can be purchased in small (about 4 ounce) bottles at the dealer for a reasonable cost. I don't know if you can find it elsewhere.
My experience with the Amsoil leads me to believe that you won't need to use any of it at all.
Enjoy the truck when you get home. Stay safe out there.
Loren