Master, what do you mean by "flat earth" for Rega?
Boss Arn, "flat-earth" is an approach to audio focused on subjective response. Flat earthers tend to do things a little differently -- like focusing more on the front end than the speakers, putting little weight on bench data, etc. The "tune dem" is an example of a classic flat earth practice, wherein they evaluate how a system "carries a tune" instead of focusing on technical details.
http://docs.linn.co.uk/wiki/index.php/FAQ_-_Tune_DemThe opposite is the "round-earth" approach, which is the conventional and scientific/structured way of doing things. The aim is largely to deliver excellent measurements in every angle. Even subjective listening done in the "round-earth" way is technical in nature (with lots of emphasis on proper placement, sharp focus, projected stage dimensions, neutrality, noise floor, etc.).
Flat-earthers want "musicality" more than "fidelity," emphasizing that a music (aka Flat-earth) system sounds like music, and that a HiFi (aka Round-earth) system sounds like HiFi. In the past, many round-earthers generally didn't consider flat-earth systems as HiFi, because they were very bothered with the "wrongness" of the output.
If we're gonna liken it to evaluating a car, the flat-earth approach is essentially selecting a car based on what makes you smile. The round-earth approach is selecting the one that delivers the best performance.
Flat-earth was coined because it's partly sticking with how things were before modern knowledge/techniques. Like how components were developed and selected before advanced measurement and design. It also references to the stubbornness of people who kept on rejecting the concept that the world is round.
In the past, there was less diversity in audio and very few companies (like Linn and Naim) championed the flat earth approach towards things. There was a time when many found this unacceptable and un-HiFi. Nowadays, the term is very rarely used as we now have a resurgence of products that incorporate flat-earth ways (NOS DACs, Turntables, Tube Electronics, Full Range Drivers, etc.). I actually see fewer and fewer purely "round-earth" HiFi people nowadays.