Only certain types of vertical blind slats are washable and even then you need to follow guidelines. If you have a stitch bond fabric that looks like the picture below then unless its been treated to be FR (fire retardant) then it should be washable.
If your blind slat fabric doesn't look like the one in the picture then we would suggest simply using a sponge an a very mild detergent mix taking care not to wet the fabric too much. Lay flat as you sponge and hang up to dry.
If however you do have a stitch bond fabric (sometimes stitch bond is plain as in the picture and sometimes it has a pattern printed onto it usually in white) then you are able to wash either by hand in the bath or by following the instructions here to wash in the machine.
Remove all the chains and weights from the bottom of the blind slats and then unclip the louvres from the headrail taking care not to break or damage any of the hangers. Roll the slats up in batches of no more than 5 at a time as tightly as you can and secure with either elastic bands or string. Place the rolls into a pillow case or several pillow cases and tie the pillow case up securely. Place in the washing machine on a cool delicates wash with no spin.
When the cycle has finished then unroll the slats and hang them up to dry over the bath or somewhere not in direct sunlight. Once dry you can hang them back at your window and re-attach the weights and chains. Your vertical blind slats should look like new.
In case everything goes disastrously wrong, you can buy replacement vertical blind slats here from as little as 99p each.
Click here to buy vertical blind slats