I don't know why you think it's an "International Airport", the name in the Airport Directory is simply "Kingman Airport".That's not necessarily true. I live near an international airport (Kingman, Arizona, USA - KIGM) that is NOT on the DJI no-fly list. Couldn't tell you why, maybe it's because this airport mainly services cargo planes and flight training, and doesn't have passenger flights running out of it.
There are 15,000 airports in the US and I doubt there's enough memory in the Phantom for that much data. So, the DJI No-Fly database just includes all airports in Class B airspace and most in Class C airspace. Kingman is in Class E airspace. If you are within 5 miles you can call the airport manager to advise of your flight. There is no control tower.
David French
7000 Flightline Dr.
Kingman, Az 86401
Phone 928-757-2134