When does Naruto learn Kurama Mode?

In his battle against the Nine-Tailed Fox, Naruto is overwhelmed by hatred and starts losing his will. That is when he meets his mother, Kushina Uzumaki, for the first time. She tells him that she loves him, which calms him and causes the hatred in his heart to be replaced by happiness. With his mother’s words in his heart, Naruto gets back on his feet and attacks the Nine-Tails with Massive Rasengan Barrage. This is a technique in which each of his shadow clones uses Massive Rasengan to attack Nine-Tails. Nine-Tails gets knocked backwards after getting directly hit by this attack. Before he could counterattack, Naruto uses his Wind Style: Rasenshuriken and attacks him head-on. The fox couldn't move due to the overwhelming firepower of the Rasenshuriken. Naruto takes advantage of the situation and his shadow clones extract Nine-Tails’ chakra from the fox's body. Naruto releases his shadow clones and absorbs the extracted chakra, entering Kurama Chakra Mode.

Infuriated by Naruto’s actions, Nine-Tails prepares to attack him with a Tailed Beast Bomb. Naruto notices his seal has changed, representing a swirl pattern on his stomach. He locks the seal, which blocks the fox’s attack in its tracks and seals it. He also restricts the fox’s movement with the massive torii. Nine-Tails curses Kushina for interfering and using her Adamantine Sealing Chains against him.

After sealing the Nine-Tails, Naruto returns to his mother. Kushina tells Naruto about the tragedy that occurred on the day he was born. She reveals that she was the Jinchuriki of the Nine-Tails before him. She reveals the fact that she belonged to a village known as the Hidden Eddy Village, in the Land of Eddies. The Hidden Eddy Village and The Hidden Leaf Village were on good terms. The Uzumaki Clan of the Eddies Village and Senju Clan of the Hidden Leaf were distant blood relatives who possessed powerful chakra and specialized in Sealing Jutsu. She mentions that her mother taught Minato various sealing jutsu. She was brought to the Hidden Leaf with the very purpose of becoming the Second Jinchuriki of the Nine-Tailed Fox, as she possessed strong chakra even by her clan’s high standards. Enemy forces feared their great power and destroyed their village,​​ and the survivors scattered across The Great Five Nations.

The first Jinchuriki of the Nine-Tails was Mito Uzumaki, wife of Hashirama Senju. When she was near the end of her natural lifespan, Kushina was brought to replace her as the Jinchuriki of the Nine-Tails. Kushina met Minato Namikaze in the Hidden Leaf, and he filled her with love, replacing the loneliness in her heart with happiness. She recalls that when she was pregnant with Naruto, she was notified by Biwako Sarutobi, the Third Hokage’s wife, that the Nine Trigrams Seal would weaken during childbirth. Due to this, she had to give birth outside the village in a secure location, under the protection of a barrier.

On October 10, the day of Naruto’s birth, Minato was concerned for her wellbeing and was struggling to maintain the seal. Meanwhile, a masked man, about whom Minato had warned Naruto during their interaction, manages to find the secure location and kills all the Anbu guarding that location.

Later in episode 329 of Naruto Shippuden, Naruto learns Kurama’s name and declares him a partner of a citizen of the Hidden Leaf Village. He then opens the seal and lets Kurama out of the cage. Kurama willingly shares all of his Chakra with Naruto. With this turn of events, Naruto acquires the full manifestation of the Kurama Mode, also known as KCM 2 (Kurama Chakra Mode 2).

1. Naruto successfully defeats the Nine-Tails and extracts his chakra. Naruto absorbs the Nine-Tails chakra and acquires Kurama Chakra Mode.
2. Kushina reveals that she was the Jinchuriki of the Nine-Tails before him. She then shares the details of her past and the day he was born.