Kirin tor is one of the hardest reputations to raise, mainly because the dragonblight questline is bugged. But i found a way to get it to exalted. It won't be easy but it's a way that allows you to do it without grinding dungeons. Just follow these steps.
1)Accept
Nick of Time
2)Do all the quests ar amber ledge.
Monitoring the Rift: Winterfin Cavern requires you to stand at the entrance of cave. Accept every single quest.
3)You should have a quest to turn in at coldarra, if so then complete remaining quests and fly to coldarra (drake sends you there if you don't have Cold Weather Flying.
4)Do all the quests in coldarra till you get
Hatching a Plan The eggs seem to reset when the server does, so you can cnoose to avoid completing that.
5)There are three important quests that you need to take (They all are completed in nexus
Have They No Shame?,
Postponing the Inevitable and
Quickening. Do these quests in RDF normals as they give you bunch of rep.
6)Head towards Dragonblight and kill
Goramosh accept quest from the item he dropped and do the questline. It works till
The End of the Line
7)Accept
The Magical Kingdom of Dalaran and do the quest following it.
8)Accept
Discretion is Key and the quest after it (It requires to slay final boss of VH)
9)Accept
A Disturbance in the West at Wintergrade Keep, fly towards Star's Rest and finish the small quest chain.
Other ways to do it:
Cooking/JC/Fishing dailies