So, after chapter 6 of Boruto: Two Blue Vortex showed Boruto using the Purple lightning jutsu to defend against Mitsuki's snakes, a lot of questions have been asked, especially: who taught Boruto that?
NCHammer, on his YouTube channel, raises 3 possibilities:
Kakashi went rogue after being convinced by Sasuke that his and others' memories have been f**ked, so Kakashi also helps Boruto master this lightning jutsu;
another is that Kashin Koji was the one who taught Boruto the jutsu because he was Kakashi opponent when Kakashi used that jutsu and might have figured out how it was created;
or that Sasuke with his sharingan had seen it once before and figured it out, passing it onto Boruto instead of the chidori.
My guess is that it was indeed Kashin Koji who taught Boruto that jutsu.
WHY KOJI KASHIN TAUGHT BORUTO THE PURPLE LIGHTNING JUTSU
It is because Dr Kataske, the scientific ninja tools researcher and genius of the Hidden Leaf, had already stored Purple Lightning in a jutsu Catridge Scroll. And we know this because Boruto used that scroll in the chunin exam against Shinki.
Dr Kataske, however was put under a genjutsu by Ao, when Ao was working as an outer for Kara, under Koji Kashin's instructions:
So, it is reasonable to assume that when Koji Kashin starts training Boruto, and discovers that the kid has great affinity for lightning style, he'd recommend Purple lightning and possibly teach Boruto how it's done: he might retrieve that jutsu by sneaking into the hidden leaf's scientific ninja tools research archives and hand it over to Boruto.
So, Boruto will use the Purple lightning in the way Sasuke used the lightning jutsu & the chidori on his sword... 6land that's how Boruto learned to use Purple lightning jutsu in chapter 6 against Mitsuki.