The wand of Kingsley Shacklebolt is of unknown length, wood, and core. It can be assumed that the wand was manufactured by Garrick Ollivander.
Like most wizards in Great Britain he most likely purchased he wand at age eleven before starting his education at Hogwarts School of Witchcraft and Wizardry.
Kingsley wielded this wand throughout his career as an Auror and during the Battle of Hogwarts. It's most likely he used this wand after 1998 as well, while he was Minister of Magic.