Q: Is "How beautiful are the flowers!" old-fasiond? In Practical English Usage, Swan says

Have you got a surprise coming!

and

Was I mad!

are spoken American English and exclamations with 'how' or 'what' are old-fashioned, but I want to ask you if that really so because.. well, just other grammar books I have don't mention these and I learned "How beautiful ~!" at a school, indeed that's a long time ago though..

A: Complete sentences which start with how or what do, in general, sound self-consciously poetic or old-fashioned, as in the case of your sentence. As always, in English, there are exceptions (don't you just hate it when that happens?). In general, these exceptions are technically incomplete sentences, and their informality counteracts the effect of the construction. Examples: "What an idiot", "How very good", "What a disaster!", or "How that takes me back".
In poetry, of course, sounding poetic is entirely acceptable.
https://www.youtube.com/watch?v=kSQdRz-HlJw
https://www.youtube.com/watch?v=A3yCcXgbKrE
