Quick question from a newbie!! 
I recently read a book called "Longitude" by Dava Sobel, which gives a neat overview of the history of the "longitude problem" or how ships might find their longitude at sea. Long story short, while latitude is easy to determine because the lines are relative to the equator and all you have to do is measure the position of the sun at noon, longitude lines are arbitrary, and navigators had the darndest time figuring out how to determine how far west of their prime meridian they were using the stars and sun and moon. Theoretically all you had to do was keep a clock on-board that displayed the time of day of the prime meridian, then compare that with local noon, multiplying the difference 15 in order to find the number of degrees west (or east) of the meridian. (For example, if your clock said it was noon in Greenwich but on-board your ship it was only eleven a.m., that means you are fifteen degrees west of Greenwich). Unfortunately, however, until John Harrison showed up, nobody could build a clock capable of keeping an accurate enough time on a rolling, rocking ship.
This fellow named Nevil Maskelyne figured out a different way, called the "Lunar Tables." He thought all you had to do was measure the distance between the moon and a fixed star at a certain time of night, and compare that with what the distance was supposed to be in Greenwich at that exact time of night on that day of the year. The difference could then allow you to calculate how far away from the prime meridian you were. It had to be the same time of night and night of the year because, according to Nevil Maskelyne and everybody else, the position of the moon in the sky changes depending on where the Earth is in its rotation, and where it is relative to the moon in its orbit. Trail and error over many years on many ships showed that he was right: the smallest error resulted in the ship going miles off course. Comparing your measurement to the wrong day in your chart could make you end up in the middle of the ocean instead of safe at harbor.
This operation seems very easy to understand and carry out if your Earth is a turning globe. It only works if you ensure that you're taking your measurement on the exact same time of night on the same night of the year as the measurement taken in Greenwich. If your Earth is flat, why would that be necessary?
Or does anybody have general comments on how sea-navigation works on a flat earth?
In good humor and good faith,
"flatcharacter"
I loved Sobel's book - I keep a copy on my "Must re-read sometime" shelf - and when I was on vacation in London last week, took a trip to the Science Museum to see Harrison's chronometers in person. They are just beautiful pieces of machinery...art meets science!
The problems with celestial navigation in a flat earth are much more basic than you've described.
Compass directions and pole-star/southern-cross directions can't possibly agree with what we know to be the case in a flat earth. This is true of both unpolar and bipolar maps - and it's quite easy to demonstrate mathematically that it'll be a problem for every possible FE map that our local FE'ers can ever come up with. It is a consequence of an oddly named theory in Topology called "The Hairy Ball Theorem" - and there is no ducking that.
(
https://en.wikipedia.org/wiki/Hairy_ball_theorem)
The final resolution of the issue of measuring longitude (using John Harrison's amazing chronometers) is that it requires you to measure the elevation of the sun and compare it with where the sun would be known to be at the Greenwich meridian at that exact same moment. With sufficiently accurate clocks, it's a simple, reliable method.
Unfortunately, the issue of the angle of the sun in the sky eludes logical explanation in a Flat Earth. When it's noon at the 90 degree meridian, the sun should be setting on the zero meridian. But on the FE map, the sun is 6,000 miles away horizontally and 3,000 miles up in the sky. This produces an angle of about 30 degrees to the horizon - not zero degrees as you'd expect.
Their efforts to explain the complete inability to achieve a sunset in their flat earth results in a pile of "explanations" - not a one of which hold water. There are claims that light doesn't travel in straight lines - that refraction bends light though MUCH larger angles and in the opposite direction to reality - and that "the laws of perspective" are incorrect! This is desperate thinking!
Hence, in a flat earth, no heading and no positional data is to be trusted - and you can't even rely on the pole star and a compass to agree with each other! Because the distances between places is "not known" to The FE Society - and they don't even have a map that they all agree on - it's hard to imagine that navigation of any kind is possible. They also deny the existence of satellites - so GPS is also unreliable.
How anyone gets anywhere in the flat earth is a complete mystery to me!
But getting our FE buddies to even comprehend the depths of the failure of their explanations is tricky.