Congratulations on your shiny new Prius! It’s a great choice, and you’re wise to take good care of your investment.
Generally speaking, Toyota’s warranty does not cover flat tires. The manufacturer covers the tires on a new Toyota, but a flat tire would only be covered if it were to be from some sort of manufacturing defect.
If you’d like additional protection for your tires, Toyota does offer additional Tire and Wheel Protection packages that will cover things like flat tires from road hazards. Ask your dealership for more details if you’re interested!