The sense from “Feel Good Blues” is that this was the Count Basie Band just having a whole of fun. There are smiles all around and Basie talks over the music a couple of times. The Count samples at least two standards (“Blues in the Night” and “Salt Peanuts”) at the start. There may be others that I don’t recognize.
Nobody was cooler than Count Basie. Check him out here and here as well.
Here is “The Count Meets the Duke” — i.e., Msesrs. Basie and Ellington — and Basie’s autobiography, “Good Morning Blues,” at Amazon. The Reprise recordings of Frank Sinatra and Basie is available at iTunes.