I would highly recommend naw tae wash yer kilt, there are cheaper versions namely the "casual kilt that can be washed as they are made from cheaper material that can be washed. Your kilt is 100% wool so should be dry cleaned, this does not fade yer kilt. I have a mate here in scotland that hangs his oot next tae the shower so the steam get at it!
I have always dry cleaned my own, never had a problem.