It seems like the "A0" refers to Arduino nomenclature. If you want the NRF52 signal AIN0, you must use connector P16, the third pin, labeled P0.02, also labeled "P0.02(AREF)" on the back of the NRF52DK board.
That labeling confused me, at least. It was not obvious to me that some of the nomenclature was Arduino. For example, one label says "(Arduino D0)". That might lead some readers to believe that only that pin label was foreign, i.e. Arduino nomenclature.
Might I suggest that you remove the "(A0)" from the silkscreen on the front of the board, and put a label in the silkscreen on the back of the board saying "All labels in parenthesis are Arduino signal names."