You have three options.

First, you can ask around, but be advised, any current or former military people on this site would be happy to see you in a kilt. If I saw a member of my platoon in a kilt, I'd be pretty stoked.

Second, you can talk to your chain of command about it. Start with your squad leader and see what their opinion is.

Third, you can just do it. It may well be that if you choose this route and you wear your kilt with pride and dignity, they will just leave you to your own devices.

But, be prepared to take a little bit of crap. Hell, I get crap for wearing a kilt and I'm an officer.