Which is right, "have a flu" and "have the flu"? And what's the difference?

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Answer

You "have the flu" or "have a case of the flu."  I have never heard anyone say they "have a flu" unless they are talking about their chimney.

Answer

"Have the flu."

However, there are some alternatives here:
I have a nasty flu.
I have a bad case of the flu.
He has a mild flu.

But never: I have a flu.

I don't know why!

Answer

Have a cold, have the flu.

A cold is non-specific, "The Flu" is derived from: "Influenza".

You can't have A flu, because there's only one type.