A spring dress is fine. My sister's boyfriend graduated from the same boot camp last fall and she wore a cute flowery dress from Macy's. Congrats to your cousin!
Wear your Sunday Go To Meeting clothes. This is one of the most important days of your cousins life. Look good and proud that he is defending your country.
Dress like you would if you were going to church. Nice, and not showing too much skin. It's not appropriate on a military base, regardless of whether or not you're in the military yourself.