I said they had extremely accurate star charts. The existence of accurate star charts does not confirm the shape of the earth in any fashion. Seeing stars where predicted by a chart simply confirms a chart is accurate.
They actually did not have accurate star charts. All they had was an idea of the relative positions of only the few stars that were visible from their own particular location.
They didn't have an idea what stars were.
They didn't have any notion of how far away the stars were.
They didn't have a notion that some of the visible star like objects were not indeed stars but galaxies, M31 for example.
They had no notion about our own solar system other than what could be observed with the naked eye.
The had no knowledge of the stars in the Southern Hemisphere.
In short their knowledge was in all reality next to nothing. What they did know was the positions of certain stars that were important to them for various reasons, mainly religious. The fact that they may have believed the earth was flat is neither here nor there given their state of relative ignorance of astronomy and much else beside. Their state of knowledge while important, as it formed a basis for both numeracy and literacy, was very limited.
Let's be clear about this until the invention of optical devices and later devices for measuring electromagnetic radiation other than visible light we were pretty ignorant about our own solar system let alone the cosmos at large. All our current knowledge we have about the cosmos is a result of professional astronomers none of which we're flat earth believers.
Thats the professional astronomers that for some reason you appear to have a problem with.