I washed our church vertical blinds in my home washing machine, without removing the chains. There were 5 windows, each with 2 sets of blinds with 10 foot drops. After some trial and error I came up with this solution.
Apart from a washing machine you need:
2 pillowcases
2 elastic hair bands
plastic covered wire (the kind you use to tie plants is great)
Some large towels
An extra pair of hands if your blinds are large.
1 Take down the blinds carefully keeping the slats together, folded one behind the other.
2 Thread some plastic coated wire through the hole in the top plastic hangers to keep them together and prevent losing them.
3 Keeping the slats together, begin winding from the weights and chains (bottom end) into a spiral, so you have something like a snail shell with the chains protected in the centre.
4 Put this into a pillow case and secure with hair elastic band. Put it into a second pillowcase and secure again.
5 Put into the washing machine drum and take up some of the extra space with towels to protect the blinds.
6 Set the temperature to 30C and delicates programme. Set it to NO SPIN to further protect both the blinds and the machine.Use maximum amount liquid detergent.
7 At the end of the cycle, remove the blinds and place them on dry towels on a flat surface. Absorb as much extra moisture as possible with the towels and pull them straight.
8 Hang them while still damp. You can steam out any creases while they are hanging..