looked at this for a loooong time, but don't have
any volume to justify more than the granite surface plates
sandpaper is crappy, got to use PSA film to keep it from 'riding up' in front of the piece
ANY rotary motion will rock the piece
far and away the cheapest is the flat lap end of a faceting machine (for gemstones)
BUT you will need at least a 8" diamond lap, probably in several 'grits'
and 10" will be FAR better, and a LOT more expensive
you need to lurk on eBay, I have seen 20" Lapmasters (the gold standard) go for $800 or so
(you do need to investigate how it is done commercially)
but you also have the cart in front of the horse (ahem, as usual NeoMoses)
-> how can you distinguish between flat - and non-flat ??
THIS is flat, to 5 millionths ! (from a yet to be released new wb)
if such flatness is a concern, suggest you get an optical flat and a monochromatic lamp to
first get some 'flatness lessons'
- then worry about how to do it