We can determine if a star is visible from a specific location using the declination of the star and the latitude of the observer, subject to other conditions like observer’s topology, the magnitude of the star, weather conditions, etc. It is possible to do this because Earth is a rotating sphere.
If the Earth is flat, every star would have been visible all night from every location. We don’t see the same stars every night because some of them are below the horizon and obscured by the Earth.
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Astrolabe is an astronomical instrument for measuring the altitude of the sun or stars, and to determine the solution of various problems in astronomy, time, and navigation. Astrolabe was used from classical antiquity, about 2nd century BC, until the age of discovery where it was superseded by the more accurate sextant, star charts, and time-keeping devices.
Flat-Earthers claim that astrolabes can only work because the Earth is flat. They are wrong. Astrolabes were designed using the spherical Earth model. To use an astrolabe, a good understanding of the spherical Earth model is required.
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