Ideas to build a stand that allows blinds to be washed?

I've had vertical blinds in the past and it is very easy to damage them if you take them outside to clean. I believe you might be ahead to place a few old towels on the floor beneath your vertical blinds and use a spray bottle filled with very warm water with just a few drops of Dawn dishwashing liquid. Start at the left side of the blinds and spray about 8-10 blinds at a time. Take a soft cloth and dry each blind (GENTLY) so you don't break the slat at the top. Dry them from the top to the bottom slightly then let finish air drying. Then work to your right and repeat. It may take some time and if very dirty, you'll need to use clean cloths as the used ones get to wet or too dirty. After you've cleaned them all, pick up the damp towels with the dirty cleaning solution that has run down the slats and launder along with your cleaning cloths.

Your blinds will look so much better and you'll know they are VERY clean. Afterwards, make a habit of vacuuming them maybe every 3-4 weeks. Hope this helps. As I said earlier, they are very easy to damage by taking them off the tabs at the top, so I preferred this method, though it was time consuming but probably doesn't take any more time than trying to do it outside. Good Luck and I hope this helps you.

You can hang them on a chain link fence for cleaning.

http://homeguides.sfgate.com/cleaning-fabric-vertical-blinds-47425.html

I hang mine over my clothes line.

Yes... a sturdy fence would work... or a clothes line or a pole or 2 x 4 between 2 ladders (would need to be the same height)

I used to put them in the bath tub and swish a rag around and then lift them out and rinse them with a portable shower head. Then devise a way to hang them over the tub until they dry. I used a long rod and hung it from the top of the shower surround.