Another Fanny Zilch cartoon turned up on youtube, KING ZILCH. This one actually has the first appearance of the character, although the regular series began with THE BANKER'S DAUGHTER shortly afterward.
This cartoon features a "Little King" and could owe some inspiration to the "Little King" series at Van Beuren, which was based on the comic strip by Otto Soglow*.
I thought some of the other characters in this cartoon resembled the type of characters that Otto Soglow drew. But Fanny Zilch wasn't one of them. I guess she owes a lot to thirties blondes, Helen Kane, and Betty Boop.
* Actually "King Zilch" is close enough to "The Little King" that it could be considered a different form of the same name.
The Little King: