You can chain the stockpiles so that the main stockpile feeds into a coal / ore stockpile that feeds into an ore stockpile, but I'm not sure if haulers will go directly to the correct stockpile or go through as many links of the chain as necessary.
They'll only carry an item one hop at a time.
The trouble with this is that if you use a lot of ore, but not much coal (say you have a magma furnace), then eventually your coal+ore stockpile gets filled up with only coal and no more ore gets to your ore stockpile because it never gets to the coal+ore stockpile. Even if you use equal amounts of coal and ore, if your coal supply is closer to the main stockpile than your ore supply, then you'll probably still eventually end up with the coal+ore pile getting filled up with just coal.
I use take chains for food and drink. My kitchens and stills are usually near the top of my fort, and each has a large output stockpile close by. A level or two down is my main dining room, with a stockpile next to it for drinks, and one for prepared food. Each takes from the stockpiles by the stills and kitchens. Down a few levels is my workshop area, which has a drink stockpile which takes from the dining room drink stockpile. Then down at the bottom next to the magma forge is another dining room with drink and prepared food piles. The drink pile takes from the workshop level drink pile, and the food pile takes from the main dining room prepared food pile. So the food flows down from the top of my fort to the bottom, as needed. But you have to keep the two chains separate, or the last pile will often end up with just drinks or just food.
I also use them for shop supplies. I'll have a small wood stockpile just above the carpenter's shop, usually 3x4. Then nearby I have a 10x10 wood pile, and the pile above the shop takes from the larger pile. The larger pile usually takes from a pile up on the surface (or just inside the front gate) that gets filled by haulers when the wood is cut. So the carpenter never has to go more than a few steps to get wood, but I don't waste a lot of space just above the shops. Before the carpenter can use 12 logs, the haulers have started refilling his handy pile and have no problem keeping up with him. Similar setups work for stones, bones, etc.