What is the best way to clean vertical blind slats?

Up and down!

You have to wash them with a wet sponge by going up and down, and up and down again, then rinsing the sponge out often if it squeezes out dirty water and go bacl over the previous blind panel..

Some fabric blinds are also machine washable, to avoid fraying however you should roll them up and put them insde a pillow case or soc