“Spirit Ryu’s” effect is considered Spell Speed 1, but may be activated multiple times in the same Battle Phase.
Other Rulings:
“Spirit Ryu’s” effect can only be activated in the Battle Step. This is where the attack is declared. Because you can activate multiple chains during this step, as long as you have Dragons in your hand, you can discard them 1 at a time to keep [using] “Spirit Ryu’s” effect. You can’t discard, say, 4 in one shot. 1 at a time and your opponent gets the chance to respond/chain. Andrew Roth, 6/21/2005