I think you mentioned writing a meta on Doflamingo. I'm really curious to know what you think about him. I read other analyses but I'd like to know what you add if you don't mind
I don't think I ever mentioned writing a full analysis on Doflamingo (at least I don't remember, but doesn't matter). It would take a really long time as I think Doffy is one of the most complex characters in One Piece. But I can tell you what I think of him, and I quickly re-read his flashback for the occasion.
Let's talk (briefly) about the Heavenly Demon, Doflamingo.
Oda is no stranger to incorporating the "nature versus nurture" theme into his work, and with Doflamingo he went the way of "born evil". In particular, Doflamingo shows several psychopathic traits, such as impaired empathy, narcissism, recklessness. He probably has a number of personality (mental?) disorders, such as narcissism for example, but I am no expert so I'm not going to delve into an in-depth psychiatric analysis of the character. Instead, I'm going to draw your attention to the fact he shows these traits since childhood, much before he went through unspeakable trauma.
As an eight-year-old kid, he asks for slaves and yells at people to bow before him, being upset when they didn't. I know he was born into an environment where this was normal, except... his family was different. He had kind parents that never encouraged such behavior, and in fact Rocinante never acted that way. Doflamingo's own brother thinks he was indeed born evil.
As I mentioned before, Doflamingo and Rocinante represent two faces of "nature" versus "nurture": they were born in the same family and, because of their father's naivety (or let's call it what it is, his sheer stupidity), they went through the same horrifying experiences. And neither of their opposite natures was broken by their trauma: Rocinante maintained a pure heart, and Doflamingo only found true strength to survive and fuel his manipulative, ruthless personality, including awakening his Conqueror's Haki. But while Corazon seems to have a relatively balanced personality as an adult, it's canon that Doflamingo shows a number of problems, like PTSD in the form of recurring nightmares, and irrational reactions to strong feelings, such as persistent laughter in response to deep anger. These symptoms do not appear when he's a kid, so it looks like his past may have greatly exacerbated his disorders.
Now, the reason why I find him so interesting is that, in spite of all this, Doflamingo does not seem incapable of love. Only unconditional love. As a child, he clearly cares for his mother and little brother, but he quickly loses the love for his father to anger, to the point he shows no hesitation in killing him and bringing his head to Mary Geoise. When he was eight. In this case, Doflamingo also shows no compassion toward his little brother, ignoring his pleads and desperation, and abandoning him to pursue his attempt to get back into the Holy Land. (To be fair, Doflamingo does not express genuine compassion ever).
Years later though, he accepts Rocinante into his ranks immediately, no questions asked and with full trust, just because he's his brother. Corazon only loses that bond upon betrayal, just as his father before him. Even then, Doflamingo is not happy about killing him. Not only it's one of the rare moments where he does not smile, but he says so himself. This may even be the instance where Doffy is the most upset before his downfall.
Furthermore, there are several occasions where Doflamingo is fiercely protective of his criminal family. He wipes away Baby 5's gold-digger boyfriends, he kills subordinates laughing at Pica, he expresses disappointment at Vergo's and Monet's death, and worry for Trebol. It's also said that all the children he took in where removed from horrible situations. Although... it's never clear whether it is sincere affection he feels. Or, better yet, he does care for them and he's ready to go great lengths to keep them safe, but it's unclear if there are actual feelings involved here. Let's look at the deaths for examples: he's the one ordering Monet to sacrifice herself, so we know that the members of his family must be ready to do so (we see this also when he claims that he'd raise Law so he'll be ready to die for him). And, although he does express regret and possibly anger at Vergo's death, we never see sorrow.
I personally think that Doflamingo is simply unable to feel empathy and genuine affection, so his egoistic and manipulative nature is inextricably tangled with the care he shows for his family. You cannot have one without the other, there is no selfless love in Doflamingo. And Oda uses this facts to take another of his recurrent themes, blood ties don't define "family", and give it a sinister twist.
These, in a nutshell, are the reasons why I think Doffy is probably the best villain and one of the most complex characters in One Piece. Hope you enjoyed my little rant!