It is traditional custom that no undergarments are worn underneath the kilt, and it is military regulation for soliders in Highland regiments. However, there are exceptions. In Highland step dancing, athletes for Highland games, and band leaders (who raise their knees to chest level as a way of keeping time) wearing undergarments is more seemly and permitted.

For civilians, undergarments is a personal choice, not a regulatory requirement. Some wear underwear, usually bikini briefs (which are easier to get in and out of when nature calls), some do not. One of the reasons that I recommended specially made kilt shirts with longer tails is that this would provide a layer between the skin and the worsted wool for those who wear their kilts in the traditional fashion, especially if they are sensitive to wool.

Last but not least, there is the answer given by all Scotsmen - regardless of whether they have underwear or not - to the age-old question of "What is worn underneath the kilt?" It is:
NOTHING WORN, ALL IN FIRST CLASS WORKING ORDER!