This is very funny—and it is an absolutely brilliant bit of musical improvisation from Louis Armstrong and Danny Kaye. I think my favorite moment is when Louis says "but don't forget Fats Waller" to rhyme off of Danny's Gustav Mahler, and without missing abeat Danny replies "I wouldn't do that" in what to my ear sounds like a Waller imitation. Genius stuff, this.
Long time readers of Hungry Blues will know that my love of Louis Armstrong began with his deep importance for my dad. I also grew up listening to and watching the movies of Danny Kaye, who was another of my dad's artistic heroes.