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 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 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 almanac showing the following declination from the North Celestial Pole:
1850: 88° 30′ 35.28″ with annual movement of 19.27″
1900: 88° 46′ 26.72′ with 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