Here's how I keep my black clothes lint free. With most of my clothes I wash them inside out and if there is a zipper, zip it up since this keeps your clothes from pilling. I use liquid detergent now instead of the powder, just because I find that the powder sometimes doesn't dissolve all the way and can stick to your clothes. Wash all dark clothes together and make sure you don't have tissues or whatnot in the pockets of your clothes/pants. And if you still get some lint, just use a lint roller. At costco they have a big 5 pack of 3M lint rollers for $10.

You can just wash your jacket seperately and just put the load on small.

If you do handwash, it'll probably eliminate lint/dust, but just make sure someone helps you wring out the jacket because I find it hard to get most of the water out myself. AND do rinse out a couple of times so that you get all the detergent out.

Goodluck, I know it can be such a hassle when this happens to your clothes, it's happened to me before and I have lots of black clothes.