Hi Roger!
On the painting there is not the Duke of Brunswick to be seen, but Friedrich II., Landgraf von Hessen-Kassel (1720 - 1785).
Behind the Landgraf there You can see a Hessian flag.
Particularly notorious Friedrich II. was due to the sale of 20,000 soldiers who had to fight on the British side against the American independence fighters in the british-american war.
With the so "earned" money, he financed his life of luxury and his magnificent buildings.
Landgraf Friedrich II. participated on the Prussian side the Seven Years' War and was initially general and since 14. May 1760 General-Fieldmarshal.
The picture is from the painter Johann Heinrich Tischbein (sen.) (1729 - 1789) and was painted in 1770.
Cheers