Linen Cloth

Linen Cloth is a cheap, rough cloth used in the creation of homespun clothes and other sundry items.

Source
This item is a drop found on humanoids up to level ~15, and some undead such as the Plaguebone Pillager in the Dead Scar.

Blacksmithing

 * Rough Weightstone
 * Copper Axe
 * Copper Mace
 * Copper Shortsword

Engineering

 * Coarse Dynamite
 * Copper Modulator
 * Rough Copper Bomb
 * Rough Dynamite

First Aid

 * Linen Bandage
 * Heavy Linen Bandage

Tailoring

 * Bolt of Linen Cloth

As a quest objective

 * Gathering Materials
 * The Tome of Divinity (dwarf 4) / The Tome of Divinity (human 4)

Places to farm
Between 5-14 level most Humanoid mobs drop Linen. The peak range is 10-14 where one can expect to kill 1-3 mobs for each linen.

If level is not an issue: the highest drop rate (60%+) appears to be from the denizens of Pyrewood Village, which are only hostile to Horde during the day, though the hostile-to-all worgen they transform into at night appear to have the next highest drop rate. But due to the time-of-day restriction and the inconvenience of the location for Alliance, the most efficient farming locations for Alliance appear to be the trolls either in Gol'Bolar Quarry in Dun Morogh, or Stonesplinter Valley in southern Loch Modan.

Alliance

 * Lvl. 7+: Kobolds in and around the Fargodeep and Jasperlode mines in Elwynn Forest
 * Lvl. 9+: Bandits and gnolls in Elwynn Forest
 * Lvl. 8-10: The grells of Fel Rock in Teldrassil
 * Lvl. 10-12: The Gnarlpines in the Ban'ethil Barrow Den on Teldrassil drop linen at a high rate.
 * Lvl. 10-12: The wendigos just north of the road in central Dun Morogh are notable in that they both drop linen cloth and can be skinned.
 * Lvl. 10-12: The troggs in Frostmane Hold in western Dun Morogh.
 * Lvl. 10-15: In Westfall, the humanoid mobs drop a lot of linen, with a high respawn rate.

Horde

 * Lvl. 5+: Undead on The Dead Scar in Eversong Woods; in particular, the skeletons in the north end near Silvermoon are east prey and conveniently located.
 * Lvl. 7-9: The tower to the southwest of Brill in Tirisfal Glades has fast-respawning "scarlets" with high drop rates; it's particularly convenient because it's between Brill and the Undercity.
 * Lvl. 9-11: Venture Co. Miners in the Venture Co. Mine east of Thunder Bluff in Mulgore
 * Lvl. 9-11: The humans in Tiragarde Keep southeast of Razor Hill in Durotar
 * Lvl. 10-11: Razormane quilboars in the Northern Barrens have higher than normal drop rates.
 * Lvl. 10-12: The Quel'dorei Ghosts and Quel'dorei Wraiths in Goldenmist Village drop cloth frequently.
 * Lvl. 12: Southsea buccaneers in the Northern Barrens near Ratchet
 * Lvl. 15-17: North of The Crossroads in the Northern Barrens, Venture Co. employees at the Sludge Fen will frequently drop 2-3 cloths, have abundant numbers, and very fast respawns.
 * Lvl. 15+: All of the humanoid mobs in the Deadmines will drop a lot of linen, up to 5 per drop.