I've done a lot of listening to and reading about jazz and it's history and that is the strangest list of so called "jazz slang", I've ever seen. I didn't even see the word "cat" listed under the "C" category. Weird list.
List looks OK to me for the period in question (1920s and 30s.) Wouldn't "cat" have come a bit later on, though - mid- and post-WWII, with bebop, the jump bands, and cool?
No, "cat" was a term Louie Armstrong is generally credited with popularizing and he was huge in the '20s.
But I do note that the list is called "Jazz Era Slang" which I suppose might mean that the slang didn't necessarily originate with jazz musicians. But if that is the case I wonder why the list wasn't just called "Popular Slang from the '20s and the '30s". Calling it Jazz Era Slang to me, implies that this slang originated with jazz music or with jazz musicians. I'm aware that I'm knitpicking.
And BTW, the period you refer to, the '40s, post WWII -- it seems to me could also be called the jazz era since the music was SO popular during those years.