I have been working on Brunswick flags of the period 1735-1754, which may have been carried during the Seven Years War, and came across this example of a captured Brunswick flag from 1712 depicted in the Triomphes Louis XIV. It is remarkably similar to the later models.
So far I have little information on the regiment, which was apparently in Dutch service in the period 1709-1713 and was 8 companies strong (acording to the Kronoskaf WSS webpage). I am currently waiting for a copy of Hall's volume on the armies of Hanover, Celle and Brunswick 1670-1715 and hope that may tell me more, which I can then add to this post.