I've never worn a kilt to work (yet!) but it's great that you already have supervisor approval. While there are others with actual experience here, let me just echo McMurdo's comment about being sure to dress neat and tidy. Don't give anyone a chance to complain.

Also, may I suggest dressing up a bit more than you might normally on a casual Friday? At least the first time. While I don't like being too dressed up myself, if I know I'm dressed really nicely then I have extra confidence and you mentioned being nervous about wearing it at work for the first time.

However you wear it, best of luck to you!