Mackay's Regiment

Were raised in 1626 to serve initially in the King of Denmark's army.
A narrative of the principal services of the Regiment, from its formation in 1626, to the battle of Nordlingen, in 1634 ; and of its subsequent incorporation with the Corps now
known as The Royal Scots or First Regiment of Foot of the British Army is online at page 128
There are some interesting titbits like the fact that there was an English regiment under a General Morgan in the Danish service. I found a reference to him in 1627 as a brave old officer of great experience, who, with four English regiments, was then encamped on the
banks of the Wasser. (source)