Complex sentence: In Austin he formed The Fabulous Thunderbirds with guitarist Jimmie Vaughan, and they became the house band at the blues club, Antone's, owned by Clifford Antone.
Split into simpler sentences: In Austin he formed The Fabulous Thunderbirds with guitarist Jimmie Vaughan. They became the house band at the blues club, Antone's, owned by Clifford Antone.