In addition to some of the historical music movies I've mentioned, here are a few more great jazz-focused movies. Some of these are streaming and others can be difficult to find. You may find DVDs available or seach the internet.
Jazz Legends In Their Own Words
A very good BBC jazz documentary filled with the BBC's archival footage and performances. There are great interviews with many jazz greats: Louis Armstrong, Duke Ellington, Count Basie, Ella Fitzgerald and more. This documentary is hard to find (like all of the BBC ones). Seek it out; it sometimes shows up on YouTube.
The Glenn Miller Story
This is a great dramatization of big band legend Glenn Miller. It captures "making it" as a musician in the 1930s. There's even mention of one of Glenn Miller's music teachers: music theorist Joseph Schillinger. Another student of Schillinger's, Lawrence Berk, founded Schillinger House music school which he later renamed after his son Lee creating Berklee School of Music.
The Benny Goodman Story
Another big band biopic on Benny Goodman. This one features a number of great musicians like Gene Krupa, Teddy Wilson, Lionel Hampton and more.
A Great Day in Harlem
This is an incredible story about the taking of the most famous jazz photo of all-time: Art Kane's A Great Day in Harlem. In 1958, 57 jazz greats all posed for a group photo. Every jazz fan needs to see this one.
The Sound of Jazz 1957
The Sound of Jazz was a TV broadcast in 1957 and showcased many jazz legends: Coleman Hawkins, Ben Webster, Lester Young, Count Basie, Monk, Milt Hinton and many more.
Jazz on a Summer's Day
Performances from the 1958 Newport Jazz Festival. This doc has an incredible lineup: Louis Armstrong, Sonny Stitt, Thelonius Monk, Mahalia Jackson and even Chuck Berry. This is one of the most highly regarded jazz films.
A 'casual' is another term for a gig. This TV series aired in the 1960s and included interviews and performances by many jazz legends like John Coltrane, Dave Brubeck, Sonny Rollins and many more. These were public TV and you may find these on YouTube.
Thelonious Monk: Straight, No Chaser
Legendary composer and jazz pianist Thelonius Monk is a mysterious figure. This documentary is comprised of long lost footage of Monk found in the 80s and gives some insight into the man and his music. Excellent.
This movie doesn't give you a detailed history of Miles Davis; this movie is a brief snapshot of a period in Miles' life. Nonetheless, this movie is excellent. It's a wild ride and Don Cheadle's performance is incredible.
John Coltrane is one of the greatest musicians of all-time. A fittingly beautiful documentary about this beautiful musical soul.