this is infact a complete phallacy

Oo err missus.

haha, oops.

Mariners have been measuring distances and plotting the shapes of continents for thousands of years.

But Round-Earth methods for topography are nonsensical. Look at this Wikipedia passage, which claims that the length of a ruler used to measure an object changes the measured length!

At some time in the years immediately preceding 1951, Lewis Fry Richardson in researching the possible effect of border lengths on the probability of war noticed that the Portuguese reported their measured border with Spain to be 987 km, but the Spanish reported it to be 1214 km. This was the beginning of the coastline problem, which is how to arrive at an estimate of a boundary that is infinite.[6]

The prevailing method of estimating a border (or coastline) was to lay off n equal straight-line segments of length ℓ with dividers on a map or aerial photograph. Each end of the segment must be on the boundary. Investigating the discrepancies in border estimation Richardson discovered what is now termed the Richardson Effect: the sum of the segments is inversely proportional to the common length of the segments. In effect, the shorter the ruler, the longer the measured border; thus, the Spanish and Portuguese geographers were using different-length rulers.

dumb method. Anyone with common sense could see this would lead to variant results.

The Romans built straight roads, proven today with modern survey equipment

This proves that the earth is flat.

No, the road is straight in the two axis of measurement of the surface of the earth. This says nothing about the flatness of the surface itself. It does however allow an accurate gauge of the distance travelled traversing the given surface

and used wheels to accurately measure distances.

That would be accurate only on a perfectly flat surface.

Their roads were flat. Of course if the earth is curved, then the roads followed curvature, therefore the wheel would accurately measure the distance travelled which would include the curvature ie: If there is curvature, measuring the path along the road will not be the shorted possible distance between two points. But it will be the shortest distance possible for the technology of the Romans. Also, the Romans generally cut through obstacles such as hills, bored tunnels through mountains and filled in valleys or built bridges, to keep the roads straight. They rarely went around obstructions but engineered ways through them.

Flight times

I call conspiracy on this one. Airlines are already known to be satanic.

meh.

ship times are another means of measuring distance

Ship times rely heavily on weather conditions and on undetectable ocean currents.

True, they are the least reliable method of calculating distance. Nevertheless many ship journeys would be significantly and noticably longer if distances were compliant with a flat earth.