No, the first sentence, "I caught a flat tire" is not used. Caught is often not readily replaceable with had.

I had never heard "catch a flat tire" until today, but apparently it's a regional usage that has the same meaning as to have or get a flat tire. It seems it's derived from French and is used in the southern US, particularly around Louisiana. https://groups.google.com/forum/m/#!topic/alt.culture.cajun/Rg6BhGrQ3uA

No, they aren't. The first sentence says "caught", meaning you're done catching the flat tire. Caught is the past tense of catch. The other sentence says "had", meaning you already have the flat tire. Had is the past tense of have, and have shows the sign of ownership (like you own something).

This is what I think. I caught a flat tire: Caught usually means you discovered something. So if you caught means you discovered. for example i caught my mistake means you found your mistake. I had a flat tire: What that means is that you know for sure that you tire was flat. Hope that helps Cheers.