Need to load up on FS to reroll. Is doing regular rifts and collecting everything the fastest way to accumulate?
Them and Greater Rifts. You need bounty mats if you want to do reforging and the cache drops FS, so might as well do them also. Nobody likes doing bounties but you’ll pick up legendaries along the way too.
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You may also use the cube to upgrade rare item to legendary. That effectively turns 25 Death’s Breaths into 1 Soul.
Wear Sage set to speed farm in bounties and rift for DB, gold and materials.
Tip: pick white items to salvage into white material. Use the cube to convert materials between white, blue and yellow.
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What Nefertiri and Maskraider said.
Also keep in mind that containers1 drop a limited number of items. On Torment XVI (T16) you get a higher percentage of Legendary items. That means you’ll see fewer Normal, Magic and Rare items drop. Especially from Rift Guardians in Nephalem and Greater Rifts.
So, if you can efficiently run T16, your best bet is to farm Bounties, Nephalem Rifts and Greater Rifts on that Difficulty. Hit all Armor and Weapon Racks you find. Salvage all items you don’t want to keep, including Legendary, Set, Ancient and Primal items.
You can use Magic and Rare items you get from Kadala to convert Reusable parts to Veiled Crystals or Arcane Dust as you need them.
I try to keep an equal amount of Reusable Parts and Arcane Dust. I try to keep double this amount of Veiled Crystals. This can be done by converting Mats when you have an overabundance of Reusable Parts and lots of Blood Shards to spend on Kadala.
Good luck and good hunting! 
1 [D3 Game Definition]
Containers: Anything that can drop loot: Monsters, Chests, Breakable Objects, Corpses, Loose Tiles, etc.