To tell you the truth, I don't quite understand trans kings and ftm drag kings. I would like to learn though. Here's my thinking. Please correct any misconceptions or stereotypes as that's the last thing I want to have for anyone, especially trans* people.
Drag kings are mostly natal females who take on a mostly exaggerated male persona for performance. They use most of the same techniques that ftms use to pass (binding, packing, masculine mannerisms) but to an extreme (adding faux facial hair, taking the mannerisms to a Marlon Brando level). It's all overdone for the sake of performance. Many, but not all, identify as lesbians.
Trans kings do the same thing as drag kings (exaggerating masculinity), but identify as female-to-male transgender (or male or what have you). And that's where I start to see a problem. How can one really tell the difference between a drag king and a trans king if both act the same, dress the same, and if the make-up/costuming is well done, look the same? It just increases the chance of the trans king getting called a 'she' and treated like a female outside of performance, something that probably (although it might) wouldn't bother a drag king.
So that's my issue with the whole thing. To me, it makes more sense for ftms to be drag queens than to be drag kings/trans kings because if we had been born natal males, that's what our form of crossdressing would have been. I realize that being a trans king isn't crossdressing, but when the audience is only familiar with drag kings and queens, it sure looks it.