Are there and if so what are the key combinations to perform the hadoken and the "multiple flying kicks" in Street Fighter 1?
The Street Fighter Wiki contains references for every move in the series.
His Tatsumaki Senpukyaku aka "Hurricane Kick" is: ⇓⇙⇐ kick
(Though note that in SF1 this can only be performed on the ground, so a "multiple flying kicks" cannot be peformed.)
 The wiki has control graphics that you may find clearer, so refer to the linked articles.