I love this idea! I've never had braces or anything, but I had a lot of friends who did and I know they are Not Fun
Kylo already has slightly crooked teeth, so I could easily see a teenaged Ben being stuck in braces and/or headgear when he was young. He hates it, hates not being able to eat some things, hates how uncomfortable it is, hates how it's another thing that marks him as 'different'. I always see him being self-conscious about his appearance and as much as his teeth were bad enough before, this is worse. He's already gangly, feels ill-proportioned, probably has acne, and this is just one more in an unfortunately long list. He already doesn't smile much by that age, but he hardly does at all now that he's got a mouth full of metal
For Hux, I could see him needing them and Brendol being an absolute ass about it, as per usual. It’s bad enough to get bullied by the kids at school, but even worse to have it home from your father, too. Alternatively, I could also see Brendol refusing to give child Hux the braces he needs due to the cost. His imperfect son isn’t worth the price, even though it would improve the one thing and Brendol could absolutely afford it. So Hux has to live with crooked, perhaps even painful, teeth until he’s an adult. At that point, he finally sees an orthodontist and is informed he needs braces if he doesn’t want his teeth wrecked and to get the pain to stop. He’s humiliated, angry that he needs something that are intended for children. How many adults do you see with braces? Even worse, the problem is too severe for the invisible ones to fix, so everyone will know
But then let’s make this the same ‘verse: adult Hux coping with needing braces but Kylo knows what they’re like and comforts and helps him with them. It sucks, sure, he knows that very well, but it’s nothing for Hux to be ashamed of. Kylo even manages to make Hux smile a few times, showing the braced teeth, because he remembers what it was like to be ashamed of his smile. He never wants Hux to feel that way, especially with him