There is no set dress code. Just casual to slightly dressy is fine.

Like Cooch said there is no dress code requirements. I have seen a wide variety of clothes worn at various military graduations/events from some people showing up in really formal dress, to some people just in jeans and t-shirts.
But many prior (or current)  military parents, or grandparents often wear their uniform.

I think of it this way... Your proud recruit will be decked out in his uniform, proud, ironed, polished, shined... Do you want to show up in board shorts and flip flops for that moment or would you like to take the same pride in appearance? It makes it pretty simple to see what the "dress code" SHOULD be. Sadly some people don't often think of it that way. But wear something comfortable and suitable for the weather.

And don't forget the camera! Wear something you want to see yourself in in pictures standing next to your brand spankin' new coastie!

Yep! I told my parents to wear something "presentable" and "Comfy enough to fly back in. That meant khakis and a polo shirt for dad, my mom wore a nice sweater (it was winter) and a pair of dressy jeans. But we had parents/family/significant others attend in a suit and tie, clubbing dresses, cowboy boots, Harley shirts with leather vests, skirt suits and everything in between. So, take everyone else's advise into consideration. Comfy, suitable for weather, and appropriate next to your dashing newly minted Coastie.

We put HOURS into just our shoes for that one moment, and DAYS into making our graduation uniform look perfect. So take a few minutes and make sure you look good too

I would just say business casual. It doesn't really matter there will be all kinds of people in all kinds of different outfits. Don't worry about it too much.