Don't put the iron directly onto the right side of the fabric at all, or it will become polished and look really bleah! Particularly at the temperature
required for pressing.

The easiest option is to press in the pleats before you sew the kilt together, so you can fold them one by one and press just the double thickness of fabric under a cloth, first the outer then the inner folds up to the edge of the fell.

If the kilt is alreasy completed then using some strips of thick cardboard or a sleeve board will help to isolate single folds for pressing.

If you have a spare piece of material use it to test just how hot the iron needs to be to make a good crease but not so hot that the fabric is altered. Do be sure to press/lift/press, not moving the iron over the pressing cloth as it will stretch the material underneath and induce waves on the edges of the pleats. Allow the material to cool before handling or lifting it, or you can make permanent finger dents in it. You can also inflict hand prints by 'patting down' obstinate bits of cloth.

Once you have the kilt pressed then don't use an iron set so high again unless you want to remove one of the creases you made.

For ordinary ironing you can smooth out the cloth on the wrong side at the lowest temperature to make a difference, then refold on the pressed folds and use a bit more pressure, so as to neaten the pleats. The inside of the fabric might become polished, but it shouldn't show. It might also improve the swing as fluffy material can cling to itself and behave as though Velcroed.

Different manufacturors use raw materials with different softening/deforming/melting points, and different resistance to heat and pressure, so you need to treat your fabric carefully until you get to know it.