This part of a sentence is correct and usable in written English.
You can use it when referring to a vehicle that has a flat tire. For example: "The car won't start because it has a flat tire."
A cab driver kneels beside his car, which has a flat tire.
LeBron James's bike has a flat tire, so he's taking a cab to see the weight lifting competition, for which, as it happens, he did not qualify.
All too often they find out the tractor has a flat tire when they need to use it; if their employees had let them know when it happened, then they could have made time to fix it and avoided frustration.
Returning to Camp Victory in their Humvee, the team encounters five armed men in traditional Arab garb standing near the men's Ford Excursion, which has a flat tire.
The handsome stranger tells her his car has a flat tire, a tight nut, and he hasn't the strength to fix it.
For example, a sick child needs to be picked up from school early, the car has a flat tire, the hot water heater has broken, the dog has diarrhea all night — you get my drift.
