I have a theory that Prince Zuko was based on a real life Scottish King from the 1400's. I haven't read the creators' tell all book but in all the online interviews I've read, they haven't mentioned any real world influences. They have only mentioned the want for Zuko to be multidimensional and not simply an evil villain but a human acting from a darker place in his past.
James II of Scotland (born 1430, actively reigning king 1447 - 1460) had a conspicuous bright red birthmark on his face. This earned him the nickname of 'Fiery Face'. The birthmark was deemed by the people around him to be an outward sign of a fiery temper.
The next alignment requires a brief recap of Zuko's mother, Ursa's history taken from the comics. Ursa grew up in a small village and fell in love with a boy named Ikem. They were engaged for a mere few hours before the Fire Lord Azulon forced her to denounce her former life to come away with him and marry his son Prince Ozai. Ozai and Ursa had two children, Zuko and Azula. Ursa wrote many letters to the loved ones she left behind. They were all intercepted by Prince Ozai. When Ursa started to suspect that this may be the case, she sent a decoy letter to her past love, Ikem. The decoy letter stated that Zuko was actually Ikem's son. Ozai became furious and threatened to kill Ikem. Ursa admitted she wished Zuko was her child with Ikem. Ozai decided he would now act as if Zuko really wasn't his son. Years later, a plot was uncovered for Ozai to kill Zuko on Azulon's orders (long story). Ursa pleaded with Ozai to save Zuko's life. The price was a powerful yet undetectable poison destined for Fire Lord Azulon thus clearing the throne for Ozai. Ursa's knowledge of the poison scared Ozai so much that part of the deal was for her to be banished from the kingdom lest she use it on him. She begged to be able to take her kids with her, to no avail. Ursa made one dose of the poison and fled. Ozai became Fire Lord but continued to treat Zuko as if they weren't related.
In my historical version, James II (real life Zuko)'s mother is Joan Beaufort Queen of Scots. The man she was still in love with is actually his father, James I, but was assassinated in 1437 when James II was 6 years old. This made James II the king but because of his age he wasn't allowed to act as King. So, simply put, whoever had custody of James could become acting king (or regent) until James turned 18. A governor named Sir Alexander Livingston was holding young James II at Stirling Castle for a portion of time to control the throne. Alexander arrested Joan and imprisoned her at Stirling Castle on August 3rd, 1439. She was released on September 4th, only after agreeing to give custody of James II to the Livingstones and give them her dowry for the maintenance of the young king.
Here is how the stories match up: the role of Ozai is played by Alexander Livingston. Whilst he was not in any way dating or married to Joan, he was James' legal guardian until their emancipation in 1449. Joan and Alexander even technically lived together for a bit (while she was on house arrest). Alexander treated James in a cold, harsh way like they weren't actually related (of course they actually weren't but this is still the case of a male custodian acting cold). Sources vary from here but it seems Alexander was imprisoned for treason around the same time as the emancipation returned the crown to James (both in 1449). James occasionally visited at least until Alexander died in 1451. Prince Zuko took to power after Ozai was arrested, but continued to seek his council from time to time.
Joan Beaufort Queen of Scots, often pleaded with her husband, King James I, for those who might be executed. Just like Zuko's mother Ursa pleaded for a young Zuko's life.
Joan remarried in 1439 to James Steward - the Black Knight of Lorn - to secure a male protector in troubled times (the Livingston/Douglas battle for custody of her son). Ursa remarried Noren who took her to get her face changed and her memories of her children removed to protect her from the Fire Nation after she lost custody (okay, okay, Noren is actually Ikem with his face changed but shhhh they're still different marriages!)
Both Ursa and Joan had to decide between a life imprisoned in a castle with their young son in jeopardy, or fleeing alone. Both pairs were reunited years later, after the downfall of the father figure that made them choose.
I mentioned at the top about Zuko's character acting from a place of darkness in his past. The darkness shrouding James II is the power struggle over his throne rights. When James II was only 10, he was witness to the murder of his two newest friends - the 16 year old 6th Earl of Douglas and his 12 year old brother. This is believed to be orchestrated in part by their uncle, James the Gross, who took over as the 7th Earl of Douglas. This heinous act exasperated a tug of war between the Douglases and the Livingstones for power over poor James' custody rights and throne. James turned out to be a good king, loved by commoners with which he socialised often. Just like Zuko checking in with his subjects often to find out how his peace efforts were going and later retiring to a smaller island. James' rule was plagued only by the murder of the 8th Earl of Douglas in 1452 in a botched attempt for James to free himself from the power struggles.
Both Ozai and Alexander were indirectly responsible for temporary crushed attempts at peace. Ozai's continued consult to Zuko fed into the abandonment of the Harmony Restoration Movement. With Alexander, he rose into favour with his son-not-son James II in 1449. Alexander pushed for the downfall of the Douglases. This could have been the start of the murder plot against William Douglas, the 8th Earl of Douglas, just a few years later.
I'm really excited to see what you think of my theory - I spent more time on this than I'm willing to admit. I discovered old Jamesy Boy down the wikipedia rabbit hole of Western European monarchy. The more I read, the more common ground I found.