It is seen that when Nagini was going to kill Ron and Hermione, Ron used a curse with a green flash. Is it the killing curse? If yes, why didn't the soul inside Nagini get destroyed, like it did in the Forbidden Forest with Harry?
Ron used a green-coloured curse, that had no visible effect on Nagini
In the movie DH 2, the curse hits Nagini perfectly, it does not miss. There is a strong possibility that it was the Killing Curse, since there are no other curses with green colour, that we know of. Yet, that does not confirm that it was a Killing Curse.
When Hermione does her research into horcruxes from the books that she stole from Dumbledore's office, she does not mention that the Killing Curse can destroy horcruxes. There are only two known ways of destroying a horcrux: Basilisk Venom and Fiendfyre. The Sword of Gryffindor was imbibed with basilisk venom, when Harry stabbed the basilisk with it.
There is no guarantee that the Killing Curse works on horcruxes. Nagini was a horcrux. I would imagine that the Killing Curse, while requiring magic and intent to kill, does not require any hard work, where as Basilisk Venom is a rare substance, and Fiendfyre requires strong control, without which the fire could turn upon the caster as it happened to Crabbe. So, it's perfectly possible for horcruxes to be immune to the Killing Curse.
Harry was not a horcrux
MA:After we got back from Carnegie Hall, we brought back your message of “Harry is kind of not really a Horcrux.”
(SU: Oh, yeah.) And I don’t want to dwell too long on Horcruxes, but I’d love to hear you talking about how he is or isn’t, or wasn’t.
JKR: Well, I’ll tell you- do you know what? This will not end the discussion.
(MA:Yeah.) (laughs) I know that, and you know that, but here is the thing: for convenience, I had Dumbledore say to Harry, “You were the Horcrux he never meant to make,” but I think, by definition, a Horcrux has to be made intentionally. So because Voldemort never went through the grotesque process that I imagine creates a Horcrux with Harry,
(SU: Mm-hm.) it was just that he had destabilized his soul so much that it split when he was hit by the backfiring curse. And so this part of it flies off, and attaches to the only living thing in the room. A part of it flees in the very-close-to-death limbo state that Voldemort then goes on and exists in. I suppose it’s very close to being a Horcrux, but Harry did not become an evil object. He didn’t have curses upon him that the other Horcruxes had. He himself was not contaminated by carrying this bit of parasitic soul.
JK Rowling has confirmed in an interview, that Harry was not a horcrux. So, the Killing curse freeing Harry of the piece of Voldemort's soul cannot be taken as proof that horcuxes are vulnerable to the Killing Curse.