Naruto doesn't need the other half of Kurama's chakra. Naruto could have defeated Sasuke with KM, let alone BM.
And to adress this, Naruto is no longer vulnerable to Amaterasu. Or, rather should I say, can't be hit by it. He can still be hurt if hit, but we've seen now that Naruto moves so fast that Sasuke can't hit him with Amaterasu. My proof being (I dont want to dig for the specific manga pages, because im tired) when Sasuke fought the Raikage at the Kage summit, Sasuke used Amaterasu on him. Raikage easily avoided it though, due to his speed in his lightning armor. Skip ahead to when Naruto faced the Raikage on his way to the battlefield, Naruto in only the standard Chakra Mode was able to be faster than the Raikage in his lightning armor. So just with the standard Chakra Mode, it would be hard for Sasuke to hit Naruto with Amaterasu.
To go even further however, when Naruto first showed off Bijuu Mode, Naruto was able to go so fast that he deflected (I think it was 5) Bijuu Damas. Essentially, in Bijuu Mode, Naruto's base speed is the equivalent to the speed Naruto used for a fraction of a moment against the Raikage, but consistent. So in Bijuu Mode, it's damn near impossible for Sasuke to hit Naruto with Amaterasu, unless Naruto was incapable of moving at all. But that's just speed alone, not to mention the variety of new abilities Naruto has unlocked since the standard Chakra Mode. Sasuke has no chance against Naruto at this point.
