Man, I should be teaching a class on this stuff... Here's my last transcription for this album, and while it's not the most electrifying solo, I feel like it encompasses all the previous ideas that I've pointed out in the other solos (air support, phrasing, rhythm, the note) so consider this to be your final review.
The melody is relatively simple and could be used as a moderate warmup. Try transposing it into all twelve keys by ear. Both sections span the octave, so make sure you focus on your air support.
You'll notice from the solo's long phrasing that the air support is constant, there aren't too many places where he takes a breath. And when he hits that high C, the tone is solid, controlled, and he still has enough support to crescendo to knock out the high Db. The idea to take away from this is that he uses the same amount of support for the high notes as he does for the low notes, it's level across his instrument.
So here are some tips for when you're warming up on long tones: Relax your throat and allow it to fill with air. Pretend that you are actually signing the notes when you play, or actually sing the notes beforehand and remember how it feels. When you're relaxed, you'll feel the air stream from your gut through the mouth. To develop your control, add volume swells to your long tones. Lastly, visualize a candle across the room and try to blow out the flame using the stream of air coming out of your horn. That's the amount of air support required to be as flexible as Trombone Shorty. Good luck.
In the meantime, let's continue to celebrate the changing of the seasons. Last week, Trombone Shorty performed with Dave Matthews as part of the NFL kickoff celebration. It was broadcasted on NBC before the New Orleans Saints football game, but I noticed that the horns couldn't be heard very well through the TV. Fortunately, there's a YouTube video shot from the audience that captures the real show. Enjoy!
Recommended reading: The Music Lesson: A Spiritual Search For Growth Through Music by Victor L. Wooten. Published by Berkley Books.