Does anyone know where this phrase comes from? I’ve always heard it in reference to water or sea when it is a flat calm - call it a ‘harry flatters’ - it’s not rhyming slang for anything as far as I’m aware.

I never heard this phrase before, or read it anywhere. Faintly curious, and momentarily idle, I tried googling it. “Harry Flatters” got about 2930 Google hits.  The first 94 all seemed to be about road racing. The 95th produced a naval association:

http://www.probertencyclopaedia.com/Z_HARRY_FLATTERS.HTM

After that dogged but otiose exercise, I gave up, remembering an anecdote I once read of a man who bought a dictionary to look up the word “coxcomb”. The dictionary entry said: “Coxcomb: a fop”. The entry for “fop” was: “Fop: a coxcomb”.

Better luck next time, moochy, and Welcome to wordorigins.org.

This sort of thing is addressed at some length in Partridge’s slang dictionary (appendix in 8th ed.).

“Harry Flatters” = “flat” with double nonsense augmentation (meaningless prefix “Harry” and meaningless suffix “-er[s]")

What Partridge calls “Oxford ‘-er[s]’” is seen in “rugger[s]” = “rugby”, “brekker[s]” = “breakfast”, “starker[s]” = “stark” = “naked”, etc.

Partridge shows “Harry Flatters” = “flat [sea]”, also “flat-out” ("fast"). Also “Harry Starkers” = “naked”, also “mad”. Also “Harry Champers” = “champagne”, etc, etc.