Ballistic Fiber is one of the very rare materials in Fallout 76. It can only be found in two different junk items that can the be scrapped for the material. You can find Ballistic Fiber from picking up the Military Ammo Bag or the Military Grade Duct Tape items.
To find these items you’re going to want to head out to the different military installations throughout Fallout 76. In the early game you can find one such military base in the southern part of the Forest Region. At Camp McClintock you’ll find Military Ammo Bags.
Savage Divide & The Mire
There are plenty of others to head to though if you need more Ballistic Fiber. The Converted Munitions Factory in the Savage Divide Region has Military Duct Tape. Camp Venture in The Mire Region has plenty more Ammo Bags.
Once you start venturing into the Cranberry Bog region, there are more military bases to choose from. You can try Firebase Major, The Thorn, Firebase Hancock, and Survey Camp Alpha which all have Military Ammo Bags and Military Grade Duct Tape.
Once you’ve gotten your fill of these items you’ll want to scrap them to get the Ballistic Fiber and make whatever it is that you wanted to craft.