Flat earthers claim Polaris is directly in the center of rotation of the sky and has never moved.
The Nautical Almanac is a publication that catalogs the positions of celestial bodies in the sky. This is a powerful tool to aid ship navigators to determine their position in the world. Accurately knowing the position of the stars is important for this measurement. Navigators use a Sextant to measure angles between the horizon and celestial bodies. A Sextant is accurate to 0.1 Arc Minutes or 6 Arc Seconds. This allows a navigator to identify their position to within one-tenth of a nautical mile or about 608 feet.
This accuracy requires the same or more level of accuracy in the information in the known positions of the celestial bodies. The information on the positions of the celestial bodies is listed by the day of the year and to an accuracy of better than 1 arc second or 0.00028 degrees.
Below are the images from the 1850, 1900, and 2017 almanacs showing the following declination from the North Celestial Pole:
1850: 88° 30′ 35.28″ with an annual movement of 19.27″
1900: 88° 46′ 26.72′ with an annual movement of 18.762″
2017: 89° 20.3′ annual movement is listed elsewhere in the almanac.
Polaris does move. So do the other stars as can be seen in other almanacs.
Nautical Almanac 1850: https://babel.hathitrust.org/cgi/pt?id=mdp.39015037941526;view=1up;seq=476
Nautical Almanac 1900: https://babel.hathitrust.org/cgi/pt?id=mdp.39015068169930;view=1up;seq=322
Nautical Almanac 2017: http://www.nauticalalmanac.net/pdf/almanac2017.pdf
Independent source for the same measurement
Annals of Harvard College Observatory, vol. 91, pp.1-290
The Henry Draper catalogue 0h, 1h, 2h, and 3h
Polaris is HD8890 its position in the year 1900 is listed on page 104 line number 90. The position is 88° 46′, agreeing with the nautical almanac.
https://articles.adsabs.harvard.edu/full/1918AnHar..91….1C/0000112.000.html

Thanks to S.C. for this citation.
Tychonis Brahe Astronomiae instauratae progymnasmata
In 1572 Tycho Brahe cataloged star positions. At the time, Polaris was about 3° from the center of the celestial rotation. It was in the Draco constellation and it was called “Polo Zodiaca Proxima”. Its location is 86° 53′.


Thanks to S.C. for this citation.
Astrognosia synoptice et methodice in usum academicum adornata c.a. 1659
A book by Ægidius STRAUCH (Professor of Theology at Dantzig), written in 1659 lists “Tycho Polo Zodiaca Proxima” at 87°. See page 152.
https://www.google.com/books/edition/%C3%86_S_Astrognosia_synoptice_et_methodice/YiK8IFp4fjgC?hl=en

Thanks to S.C. for this citation.