Kun is technically universal, and used by people of senior status addressing or referring to those of junior status. Thus, since the TTK is the superior of Fubuki, he can call her kun.
The main reason why kun is usually used for males is because traditionally they were the only ones worthy of such an honorific. It's pretty recent for kun to have spread universally.
I have heard that you help Yamakaze s... sleep every day!Hm, I do.Where are you going with this?She's turning oddly bold, this girl...I-I-I-I-I was wondering!!!If I could do the same thing! Because I'm also a destroyer!Would you mind if I did!!!!I would like to ask you a question!Admiral!Of course. What is it, Fubuki-kun?You're creeping me out.She's overflowing...It's a simple question!What's wrong? It's not like you to be so formal.