There is no flat earth measurement system which could be used to measure such distances.
There is no flat earth circumference measurement system.
You would need to use something like a yard stick.
Great R. in
"Earth not Globe" found a way: He used itineraries.
Looks like he accepts longitude values but no latitude values.
... and he terrible failed!
s.a.
The true form and magnitude of earth, by Samuel RowbothamSo in summary we have
* Presented evidence that shows the sailed distance from England to Cape Town as about 8,000 miles, whereas the calculated radius of Flat Earth is only 5224 statute miles. Not to mention, that Ireland/England is about 2,500 miles south of the North Pole (which also can be found in this chapter of EnaG) and Cape Town also is way north of Antarctica.
* And the ridiculous result, that Ireland is only 1164 miles north of Cape Town.
i found a nice example, which might be useful in this direction:
The Trans-Australian RailwayThis railway is known for world longest dead-straight track 487km, 297 statue miles, 258.1nm
between
Loongana Coordinates: 30°56′46″S 127°02′17″E
Ooldea Coordinates 30°27′33″S 131°50′08″E
Difference in longitude is 4.795° for 258.1nm, gives a total circumference derived from the railway track at 30.7°S: 19377nm (22303 statute miles)
It's not exactly what RET would predict but close, about 5% error: 18572nm