Wikipedia informs us that the Duke of Lancaster's Regiment was formed in 2004 from three regiments, one of which was the King's Regiment, which itself was formed in 1958 from two regiments, one of which was the King's Regiment, Liverpool, one of oldest infantry units in the British Army, formed in 1685.. So it's no surprise that its members became known as kingsman or that the regiment adopted the nickname for its lowest ranked NCO. The nickname kingsman is attested to by Partridge's Dictionary of Slang and Unconventional English. I expect that it would be the membership that was prestigious, regardless of rank.

Partridge notes that the nickname King's Men belongs to the 78th Regiment of Foot, formed in 1793, later (1881) the Seaforth Highlanders, a derivation not from their name but from their Gaelic motto Cuidich 'n Righ, help the king.

The OED (you'll have to check the paper supplement) does not distinguish between kingsman and King's man, and lists only non-military usages:

  • The King's Majesty's Servants, a dramatic company under James I (from 1613)
  • A Loyalist in the American Revolution (from 1809, which seems a little late since the Treaty of Paris was signed in 1783 ending a brouhaha that started in 1765)
  • A member of King's College, Cambridge (from 1803, which seems more than a little late since the college was founded in 1441)

All of the above showing both the attributive and possessive forms derived from a royal association.