Jazz flute is one of the more contemporary forms of flute playing. Of course jazz is not about an instrument, it's a style of playing, and thus can be played on any instrument. However, the flute is not a member of the traditional jazz band roster, so jazz charts don't typically include lines for the flute, unless the saxophonist doubles somewhere.
The primary reason for this was that jazz was played in a noisy environment, such as a bar or night club. The flute just couldn't project sound like the trumpet, trombone, and saxophone could.
By the 1950s, musicians began to embrace the flute timbre that was perfect for conveying a cool jazz style.
Still, flutists had to make their own way in the jazz world, as solo artists primarily, forming a combo with a rhythm section. Two of those pioneers were Herbie Mann and Sam Most, followed by Hubert Laws.
By the 1960s, musical styles were blurring and intermingling. Classical music saw a huge influx of jazz style, and the rock world heard from the flute with Ian Anderson's Jethro Tull.
For those flutists wanting a solo career, branching out into more than one style could definitely help the career along.
Many sheet music books are available with pieces in the jazz style...
Jazz was originally learned by imitating others, thus listening is an integral part of the idiom. So many CDs of great players are available today. Just take your pick...
A great way to learn to play jazz flute is through the Jamey Aebersold methods. Jamey Aebersold is one of the great jazz educators. These are lesson books with CDs that start from the very basics of jazz improvisation...