I can’t say that they help keep them clean. Some materials may ward off some of the dry dusty dirt, but usually the dirt permeates the sheet. Especially because horses are experts at being dirty. I’ve hosed down a horse in a fly sheet when both came in caked with dirt. Two for one, clean the horse and sheet. The sheet always dries quickly so it’s no big deal to hose them down and leave it out while you ride or something. Some people even put a wet fly sheet back on. If the weather is right, it will dry on the horse in no time.
I really avoid using fly sheets as it can make them hotter, potentially rub, or create other issues. I like to let them have some time in their life without clothing on (blanketed all winter), but our stable is surrounded by swamp-ish land so the bugs do get bad as summer comes. I’ve been using the Rambo Fly Buster few awhile now and find it to be durable and not too hot. Some of the cheaper options (Amigo) aren’t bad. However, if your horse is rough or in group turnout buying cheap my end up the same as buying expensive when you have to replace it. There are also differences in material. The Rambo is stiffer, yet still soft, but not clingy so the airflow is decent.
I don’t think you need two. The horse will survive without the sheet while you wash it. A good rinse with a hose and maybe a bucket of soap will do. Then a proper wash in a machine at the end of the year. It doesn’t need to be clean like new all the time.