There are three key points indicating the ‘King’ in question is in fact Master Ash, the King of Vintas. I don’t claim that this is fact, it’s still just a theory, but one that I have come to after 4 read throughs of the first two books. To understand this, though, requires some amount of character understanding.
Spoilers ahead for all of present and possible KKC books:
Kvothe is incredibly smart and does things with a specific goal in mind. Many will say that in moments of anger he will do foolish things, and that is true. But when not effected with Plum Bob, his anger is seen to be calculated and thought out:
Angry because a Master is being a dick? Does he throw a fit and leave? No. He stands, goes to the front of the class and makes a mommet. Terrible idea? Absolutely, but he knew what he was doing.
Angry because people are faking like they are your family? Go balls out and attack them all? Nope! Play the part until you can kill them all with maximum chance of success.
Now let’s look at The Cthaeh. This creature was said to be the evilest thing in all the Fae. It knows all possible futures and uses this knowledge to answer questions in a way to cause the most damage to ALL of humanity. What did this creature spend its entire time with Kvothe talking about? Denna and how Master Ash was beating her.
Now then, let’s get to the points, shall we?
Denna’s song, “The Song of Seven Sorrows”, went from paper to world renowned in the span of a few years. That’s without the aid of the internet. In the setting, who could spread a ballad that quickly besides a very high-level noble that other nobles would want to imitate? That being the case, at what level would a Vintas noble need to be to have The Song become known across all the Four Corners? A King seems likely.
Cthaeh planted a seed of unbridled fury in Kvothe. The only time we have seen Kvothe loss control out of anger was when his lute was destroyed and he called The Name of the Wind. Now, there has been jokes aid about how much Kvothe loves his music, but have we seen him show more love for anything else? Yeeeeeah, Denna seems the only thing he holds higher.
Kvothe will be armed and near the King of Vintas when he finds out who Master Ash is. In The Wise Man’s Fear we find out that in Renere all gentlemen carry their swords to court. The Maer even goes so far as to say that "It will bring the king grief in time..." about the custom. Kvothe has Caesura on his hip, the training of the deadliest warriors we know of, and a hatred for Master Ash that is completely maddening.
But there is another twist that is hidden here as well. Master Ash wants to hide his name. There’s one other person we know that is careful not to give away too much info on himself. I’ll get back to that after how I think the meeting with King of Vintas will happen. Here it goes:
Kvothe has been confirmed to visit Renere by Patrick Rothfuss. What would bring the fiery young man to the King’s Court? How would some expelled student of the University, discarded by the Maer and hated by his betrothed, a person of no real bearing, come to be invited ot the highest court of Vintas?
Well, he was brought on the arm of the King’s personal musician, of course. Denna fetches Kvothe from Imre, the two taking a long trip to the capitol together. Their bond becomes stronger than ever. Kvothe and Denna finally confess and have their first nights as a couple.
Then they arrive at court, Kvothe with Caesura on his hip. And who does he see sitting on the throne? None other than Brendon, the man who taught him to play ‘A Beautiful Game’. We are told that the Maer has come close to the Amyr and doesn’t even realize it by the Cthaeh. That’s important, and I’ll explain why in a moment. Lets get back to the story.
His wise smile suddenly seems sinister to Kvothe. He had full access to the Maer’s home. He came and went as he wanted with impunity. We are never told of the rings that he gives to anyone else and he actively hides his title and rank from Kvothe. But there is far worse things Kvothe realizes about his ‘friend’.
Kvothe comes to him, baffled. Then he stands with his cane and Denna introduces her patron. Kvothe stares at the cane and the sickly laugh of the Cthaeh echoes in his mind. He reaches out with his hand and then one of two things happen: Kvothe pulls Caesura and kills the king before fleeing… Or he begins to calculate how he will kill Brendon and escape in the night. Either way, using a Waystone he escapes into the Fae realm again, where he hides out and meets Bast.
What about Brendon being Amyr? Why does that matter and what makes me think he is?
Their credo was "Ivare Enim Euge", which roughly translates as "For the Greater Good". Brendon took an abnormal interest in Kvothe, a nobleman with no reason to show interest in a random commoner that is working with the Maer. If the Amyr are everything they are cracked up to be, would it be farfetched for him to see in Kvothe something greater than what's on the surface? More importantly, what if he knows the ‘One Story’ that Skarpi knows, and knows he must die so that Kvothe can do what the Amyr need most of all, to kill the Chandrian. What if he has to die so that Kvothe can become one of the Amyr himself?
But why did he pick Denna? What was her part in this careful dance to bring Kvothe to fruition? How else could Brendon ensure that Kvothe would carry through with what needed to be done to ascend? Well, you have to crack some eggs to make omelets, right? He had to use her to make Kvothe into the man they needed.