I made this Linen Cloth Farming guide to help out players who want to farm the cloths instead of buying them from the Auction House. I decided to search for places with high density of mobs which I can kill and drop [Linen Cloth]. I traveled around Azeroth, and after a while I made a list of places.
Westfall - Alliance
The best place to farm Linen Cloth is killing Riverpaw Gnolls near Sentinel Hill in Westfall. They respawn very fast - sometimes a new one spawns before the last one hits the ground.
Unfortunately, this place only works for Alliance players, or max level Horde players because this is an Alliance town, and there are a couple of high level Alliance NPCs there.
If you have completed the final major quest line in Westfall, ending with Return to Sentinel Hill, you cannot farm these mobs.
Silverpine Forest - Horde
Hillsbrad Worgens in Silverpine Forest drop Linen Cloth exclusively. They have fast respawn rate and the Worgens aren't that far away from each other.
Darkshore - Alliance
Twilight Fanatic mobs in Darkshore drop 1-3 Linen Cloth with 80% chance. There are always at least 3 mobs alive and they are close to each other.
Azshara - Horde
Good place to farm Linen Cloth are the Restless Spirits in Azshara. Most will drop one to three Linen Cloth.
If you are unable to farm at any of these places because you have done the quests, just go to my Wool Cloth farming guide. While farming Wool Cloth, you will get plenty of Linen Cloth, most mobs drop both of them.