Never could wrestle a kilt on the ironing board. Ham's method of laying it out on the floor is what I did until I found that a steamer takes about 2 seconds to disappear wrinkles.

I like to hang the kilt on a hanger and pull the bottom of the pleat firmly to help the steam set the pleats when working on the pleat side.

Steam is the answer - whether a hand steamer, a big steamer, or hanging it in the bathroom with the shower on hot.