I have never heard the expression, "punctured pneumatic." I am wondering if you are mis-translating pneumático to pneumatic. In U.S. English, pneumatic is not a synonym for tire. Pnuematic refers to any tool that uses pressurized air, like a pneumatic drill.
In any case, flat tire is the most common expression.
After doing a quick search, I saw that technically a pneumatic tire refers to any tire that is inflated with air. But again, pneumatic is not used (colloquially especially) as a synonym for tire.
A tyre can be flat without being punctured; it may not have been inflated properly, or the air may have escaped from the tyre via a leaking tyre valve.
On the other hand, a puncture is a hole or tear in the tyre surface, usually by a nail or other sharp object piercing the tread or sidewall.
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In this thread, there is only mentioned the usage of the expression "having a flat tyre" and "having a puncture". I have heard here many times how context is important. So I put the expression "get a flat" and "get a puncture" into different sentences to find out if the usage is possible or if it sounds wrong.
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In casual American English, any tire that has lost enough air to make it worth adding some air is a "flat tire." It doesn't need to be literally flat (completely deflated). You can tell that it's been punctured because it's "flat" (technically just low) so we don't bother with "punctured" . We can say "My tire looks a little flat. I think I'll put some air in it tomorrow."