These traders, one ship and one caravan will buy goods, but they won't sell me any barley. I've got room in my storage yards, and they're set to accept it. Each year since I've opened those trade routes I've sold 0 of 2500 available barley in spite of setting my overseer of commerce being set to import to maintain 1000 units of barley.

What's going on?

Hmmm that's weird. Do they have a lot of business at the docks, importing/buying other things? Because, at least in Caesar 3 there's a time limit for how a long a ship spends at a dock. I'd assume it's the same case for Pharaoh, so all the warehouses your dock cart pushers would want go to should preferably be pretty close to the dock.
I'm not sure about the caravans though. They might not like walking long distances between different warehouses in your city. Just to experiment you can try to set a warehouse visited by them to accept barley.

Traders will walk as far as they need to, in order to trade their goods.

Have you actually set the overseer to import the items? For docks, do you have enough docks to handle the traffic, as too many boats around one dock will mean some traders will just leave the map?

Please upload a save-game file to the forum so others can assist with the issue. :)

Actually, I was wrong. Both traders who sold these items were land caravans, but in any case, my docks were working fine for other items. I had everything set up correctly to purchase, as I had in previous scenarios. They were buying things from me just fine, but not selling barley, beer or flax. The donkey guys were going to my warehouses. Each year, I'd have 0 of the available number to purchase.I needed these things to upgrade. The scenario appeared to be bugged, and I finally gave up and used the cheat to bypass it. The subsequent ones are working all right.