In this clip, we see Fletcher back in his apartment, alone, and enjoying jazz music with a faint smile on his face. It’s the most positive expression we see him throughout the whole film.
Imagine we attach this to the end of Whiplash. After Neiman nails his debut solo, we smash cut to black for a few seconds. Then, we play this scene.
While we see Fletcher satisfied and happy (and also revealing some intimate details of a character we’ve only seen one side of throughout the film), we are also aware of the loneliness of his apartment (and presumably his life). It’s good foreshadowing for Neiman’s character, that even though he achieved his goal, that may not be a completely happy ending.