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Just look at this handout from the local Shoppers Drug Mart.The baffling thing is that the wall poster in the store has "flu" spelled correctly. It's as if someone scanned the poster, shrank it down, redid the text to include a typo (twice), and then reproduced it for distribution. I'm thoroughly baffled. (At first glance, I thought that it was an ad for a chimney-cleaning service, but no, the French translation uses the word "grippe", which is still occasionally seen in English.)

"Flu" is a contraction of Italian "influenza", "influence", which in turn came from Late Latin "influentia", with the same meaning, because the illness was believed to be the result of the influence of malign stars (astronomical ones, that is).

Although nobody is absolutely sure, "flue" seems likely to be related to Latin "fluere", "to flow". It looks like a slam dunk, but "flue" was originally spelled "flew", and has a number of other possible sources.

"Fluere" is related to such words as English "fluent", literally "flowing", and "confluence", the flowing together of two rivers into one, and of course "influence" itself. That doesn't mean that "flu" and "flue" are interchangeable.