My advice is to gradually phase it in. Pick a normal location or activity and wear the kilt. when you have gotten a little more comfortable being kilted there, pick another.

The first place I wore my kilt that didn't involve friends or family was for a quick run to the grocery store. No one seemed to notice. It helps to just do mundane everyday things in your kilt. It reinforces the idea that it is just another piece of clothing. And it doesn't take long before you stop thinking about the kilt and start focusing on the task at hand.

If you are feeling incredibly self conscious, start small. Go out for ten minutes and run an errand. You don't have to go full time kilted all at once. As long as you keep pushing forward, it will get easier.

If you are having trouble making yourself do it, then just pick days to wear the kilt, throw it on in the morning (or after work if necessary) and just go with it. Whatever you're gonna do that day, do it kilted or not at all. Don't give yourself the option to wuss out.