<<A flag resource for the Hessian Jaegers would be appreciated too!>>
Jaeger did not carry flags/colours; the dispersed nature of their work and their tactics made them pointless in battle, and vulnerable to capture.
The two-battalion Anhalt Zerbst "regiment" was a bit of a mish-mash, having one battalion of what appears to be line infantry in Canada, and another of "pandours" (apparently recruited in appropriate parts of the Austro-Hungarian empire) who served in NYC. It seems unlikely that the latter would have had flags anyway, but there's no record of the line infantry having them either. Bear in mind that these were new units raised specifically for the war, and not part of the existing forces of the state.
As the OFM says, the flags on the link from Dale are the modern heraldic arms of the regions. They may – or may not – have a history going back to the 18th Century, but be aware that many such state flags across Europe have had regal/noble elements stripped from them since the early part of the 20th Century. The arms on the A-Z flag might have featured as the central emblem on any colours presented to the A-Z regiment, but it's highly unlikely that the regimental flag would have been as shown.
Here are the 18th Century arms of A-Z:
link
On a point of useless trivia, the ruler of Anhalt-Zerbst during the AWI was the brother of Catherine the Great.
