I suspect you want to buy dyed cloth/thread from caravans and use it to make clothes. Sadly, stockpiles can't distinguish between those, though as anewaname says you can adjust standing orders.
Now, worth mentioning regarding textile industry:
Thread is so light that you can stack 75 (the maximum) into a workshop before it gets cluttered.
This means that using stockpiles as in-between place usually just creates an extra hauling job and some stalling - though granted, you can stockpile the thread/cloth two tiles closer with proper planning if you don't mind pulling a hauler from tavern to move 1 item 2 tiles.
In current case, to make workshop-workshop links, you need to make burrows restricted to the area only. A single workshop can take from every burrow it is restricted to, so it's up to you to make one or more.
However, should you have thread or cloth stockpiles elsewhere, mind that this doesn't stop those stockpiles from pulling from workshops - unless you link those workshops to give to, say, 1 tile coin stockpiles.
@carnivorn:
Well, dwarves definitely can use items from carpenter's workshop linked to stone stockpile right now, for instance.
Running out of bags is rather common affilition, however this is because dwarves compulsively store seeds in bags, and as you get several seeds from 1 plant unless cooking it the number of seeds tends to increase until you hit the cap.
Of course, even if they can use bags from dyer's workshop, if you keep making more bags and making them accumulate in Dyer's workshop it'll eventually get cluttered.