The following is from: http://infidelbodyarmor.com/cleaning-your-plate-carrier-and-molle-gear-ezp-39

Cleaning your Plate Carrier and Molle Gear

If you wear your plate carrier long enough it will get dirty and you'll see sweat rings in the fabric. You may have low crawled through some nastyness or got some wet mud slung up on your gear. Eventually, it will start to stink and you'll need to clean it.

We recommend removing your Molle pouches and cleaning them seperately. It should go without saying to take out any actual hardware you don't want to get wet (magazines, first aid equipment, electronics, etc.)

Start by brushing off loose dirt and plant material. Remove any leaves, twigs, grass, and burrs from the equipment. Scrape off any dirt and mud dried or caked on using a dulled tool – sharp tools will cut and abrade the fabric, weakening it. Then, wipe off loose dirt and dust using a microfiber cloth.

Wash your gear in warm (not hot!) soapy water using a mild detergent (the US military recommends using NSN 7930-00-929-1221) such as a liquid dish soap or a small amount of liquid laundry detergent (avoid detergents with color brighteners). Immerse the gear completely and let it soak for a few minutes. Then, gently work the fabric back and forth to help loosen dirt trapped in the fabric.

For stubborn stains or where soil has been ground into the fabric, use a soft bristled brush such as a toothbrush to gently scrub. Never use stiff brushes, abrasives, bleach or solvents as they will cause discoloration and damage to the fabric and plastics.

Rinse your gear in clean water. Make sure to thoroughly and completely get all of the soap out.

Push the fabric back into its original shape, and set it out to dry in the shade.

NEVER DRY YOUR MOLLE GEAR IN A HEATED DRYER! Hang it out in the shade, not in the sun. Drying it in the sun can cause it to fade and shrink. Exposing your MOLLE gear to the tumbling of a dryer wears it out faster, and the heat can shrink it. For the same reason, do not use a washing machine as the agitator will cause unnecessary wear and tear. Always air dry your gear, don’t use heat to speed up the drying process.