Why didn't Sasuke use Amaterasu on Kaguya? Amaterasu is powerful. Sasuke just had to secretly, when Kaguya was busy with Naruto, cast it on her. She would have burned to hell.

But why didn't Sasuke use Amaterasu on Kaguya?
Given she be the first to wield chakra, Kaguya can absorb any technique; including the Amaterasu


  As the first person to ever wield chakra, she can absorb any technique that she encounters


However, towards the beginning of Naruto's and Sasuke's battle with Kaguya, Sasuke did use the Amaterasu on Kaguya to distract her


  To create an opening, Naruto convinced Sasuke to attack Kaguya with Amaterasu, which allowed him to get close to her and use his Sexy: Reverse Harem Technique. The technique was successful in distracting Kaguya long enough for Naruto to strike her


You can see this occurrence on Youtube