Unfortunately, flat tires are a fact of life in driving cars, and you as a traveler are responsible for a flat tire that occurs during the trip, as well as any related damage that may result from that flat tire.
The only exception to this policy is if it is professionally documented that the flat is the result of a tire that was either 1) defective, or 2) had been subject to excessive wear such that it was unsafe to be driven as of the start of the reservation.
In the event of a flat, the traveler should look to a spare tire (our roadside service can dispatch a provider to help with this), and then coordinate with the owner to determine how to resolve the tire issue. If a repair is appropriate, that may be an effective way to go. If the sidewall is damaged or a repair is not possible, the renter is responsible for replacement of that tire (without any reduction or pro-ration based on mileage), but is not responsible for replacement of any of the non-damaged tires. The traveler needs to get the approval of the owner for a replacement tire, and must replace the tire with one of equal or greater quality.