Destiny: The Taken King has a number of new resources for players to collect, which are required to upgrade certain weapons or complete certain quests. One such resource is Hadium Flakes, which are required for the Exotic Sword quest. Another is Wormspore, which you'll need to upgrade both Legendary and Exotic weapons and armor in The Taken King.
Hadium Flakes can only be found in chests located in Dreadnaught Patrol. You'll also find Wormspore in the same areas. You can identify Wormspore as a glowy, green object.
To maximize your farming efficiency, you'll want to collect both Hadium Flakes and Wormspore at the same time while following a circuitous route in the area.
It's hard to give directions without presenting a video, so I'd recommend watching the following video from YouTuber Th3Jez, who details the farming route for both Wormspore and Hadium Flakes perfectly.
Do not follow any guides that instruct you to return to orbit with each run. Both the chests and Wormspore respawn and reset on their own, so you can do this indefinitely.
If you follow these instructions, you'll be able to get 25 Hadium Flakes within 30 minutes.
Be sure to check out our guides on the fastest way to earn Legendary Marks, Infusing weapons and armor, the fastest way to raise your light level, and how the Exotic Blueprint system works.