Phasma, who killed his father for Armitage, is a partner in crime for him. They know each other better than anyone in First Order. And even if Hux is proud to say he knows something about Phasma which others don’t, still is unable to see “though her helmet”. She would never allow him to see how she sees her own allegiance to the order. Armitage doesn’t ask though, believing in Phasma’s loyalty, after array of favors she did for his career.
I can see them having some sort of secret brotherhood, a one, that – for example – would cause Phasma to laugh from Hux’ inside jokes, as she would be only to understand them. They are both really good liars, one better than the other. They know that but they both feel good in each others’ company – a buddy friendship, war crime friends, however you call it.
She is still lower ranked than him, but I can easily see them chilling after duties, when Armitage pours his bitterness, while she just silently listens and watches him, remembering all of this, probably to use it later.
I like unspoken dynamics between Hux and Phasma. The film didn’t show a lot of it, ugh, didn’t show at all. But fandom provided where the screenplay failed. It can be tragic, it can be evil, it can be amusing – Hux with Phasma is just a good chrome ginger duo.