I have been washing by hand and using the Nikwax waterproofing and was going to respond with that, but your question got me to wonder if I was doing something wrong. So I called Klim Customer Service and the person said to:
Take the pads out, then zip it up and fasten all the Velcro doo-dads.
Throw it in the washing machine on gentle cycle, using any gentle detergent. She said that the ONLY thing to avoid was anything with any sort of bleach, and some laundry soaps do have some for that "extra whitening power." I've been using Woolite and she said it would be fine.
Do an extra rinse to make sure all of the soap is out.
The Use & Care instructions say:
After your gear is dry, spray it with water from a bottle or sprinkle some on with your hands. If it beads up and rolls off the gear, you're good-to-go. Go riding! If it soaks in quickly, it's time to re-apply. KLIM and GORE-TEX(r) recommend spray-on DWR treatments like Revivex. This type of DWR is heat-activated. You spray it on your garment's exterior after the wash cycle and toss it in the dryer like normal. Follow the instructions on the bottle. Wash-in DWR treatments are not recommended as they coat all surfaces with the DWR and can negatively affect comfort and performance.
Dry on warm- then on hot for the last 15 minutes. This re-activates the jacket's waterproofing, and if you use Nikwax waterproofer the heat is necessary to activate that.