Flag attributed to the Confederation of the Rhine by "flaggenlexikon.de"; the source itself states that "it isn't known exactly" if the Confederation had an official flag. This particular design is cited as the "alleged" (angebliche) flag, but no source as to the source of this "allegation" is given.
The design has been online at flaggenlexikon since 2004
In 2023, the author of flaggenlexicon gave the following comment after an email inquiry:

"Now you ask me from where I got the picture of the flag. Unfortunately, I can not tell you. When I started the Flaggenlexikon, I worked without any sources at all. It was a small hobby project that grew and grew. Later I worked on the sources. When I revised the Confederation of the Rhine, it was no longer possible to keep track of it. But it is a fact that the Confederation of the Rhine certainly did not have a flag. That is why I have kept the flag mentioned, pointing out this fact, and the word "alleged" was added from the beginning. It is regrettable that facts are created from this, but for me it is also part of the process of gaining knowledge."
http://www.flaggenlexikon.de/fdtlhirb.htm#Flagge
N3MO