Go tubeless, and that will greatly reduce your chances of flat tires. I've had my gravel bike for about 6 months setup with tubeless tires from the start and have not had a single flat tire. I would get between 1-2 flats a month riding a similar course on my road bike with 25mm clinchers, not including the off road segments I am now able to ride.

The Stans NoTubes system is the way to go, look into their excellent Grail wheels.