Use your blow dryer to blow dust
Place silk flowers or the silk arrangement in a large plastic garbage bag. Pour in some pickling salt (about 1/2 cup) and shake the bag gently up and down ensuring the salt moves around the flowers. The salt will scrape away the dust. I do this once a year with all of the silk plants in my home.
@Liliana Wells I can't speak knowledgeably about kosher salt but I think it should be OK because like @Tabby said you want a coarse not fine salt. I don't use water on my silk flowers/arrangements because I find the dust can turn to 'mud' when mixed with water creating more of a mess. Try it with just one flower and see if you are happy with the results.
For years I have put my silk plants (no flowers, just greenery) into a lingerie bag in the washer on the gentle cycle, cold water, no soap (unless they were in the kitchen and had greasy dust - then a small amount of something mild, like Dreft baby soap). Then I let them air dry - usually in the driveway or the yard on a sunny day. They dry fast and look brand new. I have lost a leaf or two each time...sometimes I can put it back on the plant, mostly it's not noticeable.
Hose them off if they aren't in arrangement. And let them dry in the open air. Or use Silks Alive Floral Spray if they are in an arrangement. We used both ways in our flower shop!
It depends on if they are in an arrangement or single but i use an air tank and spray them with air or caned air for delicate areas if realy dirty you can wash them in the sink with a soft toothbrush (pick the flower's or leave on depending on arrangement or not) then set aside to dry or place in pillowcase and dry on low. You don't want to melt the plastic. After you get it clean get a can of Aqua. Net hairspray and spray your flower's then all you have to do is go outside and shake them to get the dust off. Works on silk ivy too.
I put a plastic bag around the vase/pot to cover the base, if it is an arrangement and swish the flowers in warm soapy water, then rinse. Let air dry.
I am not sure about this so test it first as it has been many years since I had silk flowers or any flowers for that matter but place in a bag and add salt and shake , it should remove the dust.
I've always just put them in the dish drainer and gently sprayed with the kitchen sink sprayer. Then let them dry out in the drainer too.
Put them in a Dryel home dry cleaning bag and throw them in the dryer. Works like a charm and will even bring the aroma back to old eucalyptus.