Just about all irons you'll encounter today have a wool setting, and a steam function. So I wouldn't worry about putting a towel in between the iron and the kilt. That's more of a concern to moderate the temperature on older irons.

I'd just use your regular ironing board and work a few pleats at a time. The original crease lines for the pleats should be there for you to work with. If you grab the bottom of the pleat and tug on it gently while you press, it will help give some tension and keep the pleat straight.

Just use lots of steam, a little bit of pressure, and there you go!

M