#indoctrination doesn't exit

The Fire Nation line of succession

When it comes to royal lines, there were multiple elements that went into setting the line of succession: descent, sex, legitimacy, religion etc. For the Fire Nation, the ones we have 100% confirmed are descent and legitimacy (this last one seen with the Camellia-Peony War, where Chaejin was excluded from the succession because he was born out of wedlock). I would have gone on a whim to say sex counts as well, however, it is a bit foggy. In the Reckoning of Roku, it is mentioned that Firelord Taiso believed Zeisan (Sozin's younger sister) would have been a more competent ruler but could never become Fire Lord due to being a nonbender (I didn't actually read the book, so if someone who did wants to pitch in with the exact wording, please feel free to). This implies that being a Firebender is a requirement, but being a woman isn't. However, it also implies that Taiso would have been fine with ignoring the descent part (Sozin was older) if he deemed fit. Skipping the firstborn in favour of the second one isn't unheard of when it comes to succession so sure. And he is the absolute monarch, if he wants to pass papers to change the line of succession, he can. It is unclear to me if there is any power in place to veto or block a Fire Lord's ruling on any matter so for all we know, if he wanted, he could have. Plus, the fact that Ozai got crowned over Iroh because it was 'Azulon's dying wish'. For the religion part, it seems like the Fire Sages have to perform the coronation and acknowledge the monarch.

So to make it more digestible, the line of succession (while Azulon was still alive) is: Iroh → Lu Ten (firstborn of the heir) → Ozai → Zuko → Azula. With Lu Ten dead, Iroh MIA (at the time) then we have Ozai → Zuko → Azula. When Iroh came back, he gets added at the end of this line of succession. I am a bit unclear on Iroh in current times because it looks to me like he rescinded his role in the line of succession altogether with deciding to live in Ba Sing Se and letting politically inexperienced Zuko rule instead of taking over for a few years to create some stability.

Right now, we have Fire Lord Zuko and his heir presumptive (aka an heir that can be displaced if the monarch has children) Azula. Unless he wrote a decree to take her out of the line of succession — which would require a lot more brain cells than the writers are willing to give Zuko, not that he had a lot of them when it came to politics to begin with —then she's next in line. It doesn't matter how much anyone wants it or not, if Zuko drops dead tomorrow, Azula gets the throne.

Now, onto the other matter.

How does one become a Princess?

Option 1: You marry into the royal family. For example, Ursa was styled as a Princess, as she married Prince Ozai.

Option 2: You're born in a royal line. For example, Azula is a Princess because her father is a Prince, her grandfather, at the time of her birth, was the ruling monarch of the Fire Nation etc.

Bonus Option it's complicated: Royals had a habit of having children out of wedlock sometimes. Said children, if acknowledged, could be granted titles (Count of X, Dutchess of Y etc.) . Getting acknowledged and a title does not automatically put you in the line of succession, though. For example, Firelord Chaeryu was forced to acknowledge Chaejin and avoid dishonoring his noble mother and her house, but he excluded Chaejin from the royal family.

So Kiyi is not a Princess. Simple as that. Neither of her parents are of the royal line.

Could she become a Princess?

Well, this gets interesting.

Let's start with the fact that Kiyi got a pretty bad deal in a class-based monarchical society.

First thing, while her mother is a noble, her father is a commoner. Even if Ursa's family became destitute after Roku's death because of political reasons, it does not change the fact that she is still nobility unless Sozin revoked Rina's title, which I am not 100% sure he did. We don't know anything about Jinzuk besides the fact that he was the magistrate of Hira'a. While magistrates do not have to be part of the nobility, they can be. He could have been a second/third/fourth son of a small noble family with limited power/resources, given the position he was given was in a place like Hira'a, which is what I am inclining towards. He could have also been just some guy, but someone appointed him, and as a rule of thumb, you don't just go into the street and pick a random person to appoint to an administrative and leadership role, even if it's a small town. Given that Azulon was set on Ozai marrying Ursa because she was Roku's granddaughter, whether or not Jinzuk was a noble, it doesn't matter all that much in the grand scheme of things. However, in Kiyi's case, it does if Zuko wants to give her a title. It's more stigma than anything because people can be given nobility titles for specific services to the crown etc. But this is not her only issue. Which leads me to...

Second thing, Kiyi is a bastard. Which, in my opinion, would hold even more stigma than her father not being a noble. Ursa never divorced Ozai. As far as we know, polygamist marriages aren't a thing in the Fire Nation, so her marriage to Ikem/Noren is invalid. Could she be granted a divorce retroactively by the Fire Sages? Actually, yeah. Because Zuko named Shyu as High Sage, which was like the one sound political move he ever did tbh. We don't see what the Fire Nation's stance on divorce is, but given that Shyu is a Zuko loyalist, he'd probably grant Ursa retroactive divorce from Ozai. I am not a legal expert, however, as far as I know, retroactive decisions tend to be reserved for correcting a mistake or omission in the written record. She was still married to Ozai when she went and married Ikem. Though technically, she married him under a fake identity (and so did he), which might make the marriage void regardless in the eyes of the law. Idk how Spirit involvement affects legal matters in the world of Avatar, but as things stand right now, unless we pretzel-twist ourselves to make excuses, Kiyi is born outside of legitimate wedlock.

Now, Zuko might not care. In fact, he probably doesn't. He could still give Kiyi a title, including that of Princess. It was not uncommon for illegitimate relatives of rulers to be offered roles/titles once acknowledged. The real question is if he would put her in the line of succession. Kiyi has no business being there because she does not have royal blood.

Could Zuko do whatever he wants, give her the title of Princess and shove her in the line of succession while taking Azula out of it for good measure? Sure, he can. He'd probably love that, in fact. But that leaves two things open.

One, nobility would not take kindly to a bastard child of a commoner with no royal blood being in the line of succession. If we also add the angle of taking Azula out of it, it would just increase their ire. There is already a long list of why the nobility is probably angry at Zuko (and should attempt to assassinate him a lot more than they do), but I think this one in particular has other implications. There might be nobles who are neutral about Zuko. Shamelessly discarding societal norms on a whim might make their perspective swing towards negative. It could make him lose goodwill he might have or potential allies.

Two, it will make the commoners wonder. If this random girl, raised as a peasant, with a commoner father, born out of wedlock, can be put in the line of succession just like that — while discarding a princess of the blood if we are at it — then… is the royal line not that special? The whole premise of a monarchy is that the monarch and their descendants have the divine right to rule. Being part of that bloodline gives you the right to rule. So if that can be discarded, if that bloodline is not all that important… should Zuko be Firelord? And most importantly, does the Fire Nation really need a monarch at all?