One of the first styles of music that any aspiring flutist should encounter and study is Baroque music. The Baroque music period takes place approximately from 1600 to 1750 A. D. In this period you will hear from favorite composers like Antonio Vivaldi, Georg Philipp Telemann, George Friderick Handel and Johann Sebastian Bach. Playing music from this period helps to establish good phrasing skills. The music will also expose you to the use of ornamentation and improvisation.
Building good improvisational skills starts with the study of the Baroque period music. During this period composers would add a host of symbols to their melody lines specific to different types of ornamentation. The trill (tr), the mordent and the turn (~) are good examples. The symbols served as a sort of shorthand for composers and players. In other words, the composers embellished their music without writing so many notes. And much like the use of jazz chords or chord symbols, composers would make use of the figured bass to fill in harmonies in a keyboard arrangement.
Below is the Sicialiano from the Sonata in Eb Major, BWV 1031 that I recorded for my Bach, Handel & Mozart Flute Sonatas CD. This recording made use of the harpsichord for accompaniment. Below I have also included the play along track. Click this link for a .pdf of the flute music> J. S. Bach: Siciliano