A silk kilt would be interesting. Now as for the weight of it. I would think that it would be possible because silk does come in different weights. Silk has been used for everything from undergarments to furniture fabric. It would just depend on the weight and if you were rich enough. Also from my days when I used to section hike on the AT, one of the things I used to have as part of my gear was a silk lining to my sleeping bag.

It helped me retain warmth but in the summer months when I would go hiking I could reduce weight by leaving the sleeping bag at home and having the liner to sleep in. So I would think that a kilt could be the same.