They want independence from India, with some of them wanting to be with Pakistan. From what my IOK friends have told me (and my general knowledge as a Kashmiri), when the Pakistani flag is waved, 99% of the time it's just to rile up the Indians, they don't actually want to join Pakistan, they just want independence. Same with when they wave an ISIS flag. I have made this conclusion based on people I know, the news, the fact that India won't hold a vote, has over 700,000 troops there, etc.
I won't be visiting India anytime soon, not really interested as I don't see it as much different than Pakistan and because the fact that I'm Pakistani will get me some prejudice and he fact that I'm Kashmiri will cause some of the people to constantly badger me about what I want for Kashmir (just like in real life when I meet Indians at party's).
One mans terrorist is another mans freedom fighter, I am sure you are familiar with the saying, no?