I have 2000 flax in storage and ten weavers, none of which have flax. It's driving me crazy.

Is flax being stockpiled ? Is the storage yard being set to "Get Maximum" of flax ?

+1 question: Is there a continuous road connection between the warehouse and the weavers?

Do the storage yards containing the flax have other tasks which they're doing first? If your city arrangement allows it, try making a storage yard by your linen production which only accepts flax, and block flax from entering your other storage yards.

Only issue is if you're importing the flax by river and your linen production is in a different area to the your docks, then it may take some time for the docks to handle ships selling flax.