Actually, as an American, I think it's perfectly fine to refer to the car as "it." If you did ask me what was wrong with the car, I would say "It has a flat tire." However, I know some people who like to refer to cars like females and say things like "Ain't she a beaut?" So, I wouldn't be weirded out by either "She has a flat tire" or "it has a flat tire." I agree that I would also say "oh no, I have a flat tire." I thimk these are all understandable, legitimate ways of saying this sentence, I don't see why there is such a conflict.
Now, what I came here for was to see how "pneu" is supposed to be pronounced. Is the "p" silent?
There are many variations of English and what is common in one region may not be common in another. In addressing one another on the forum, please be sensitive to that fact and always use respectful language. Belittling others will not be tolerated. We are here to help each other learn French, not nitpick English.
The French native who wrote this sentence did intend to refer to a car as that is most natural in French. However, some English speakers do refer to their cars as "she." In addition, in some regions it is common to say "I have/you have/she has a flat tire/tyre," rather than say "I have a flat tire on my car." The last part is implied. The owner of the car is indeed also the owner of the unfortunate tire/tyre.
For these reasons, "she" will be accepted as well as "it."