In middle school, they had sparred once which resulted in Kinji (under the affects of Hysteria Mode) subduing her effortlessly. Because of this Fuuma has a great deal of respect for Kinji going as far as calling him "master" when ever addressing him. In Volume 10 of the main series light novels, it is revealed that she is Kinji's Amica.
In the AA spin-off, it is revealed she had been Kinji's amica well before Akari became Aria's.
As a friend of Kinji's and one of the top students, Fuuma holds a great deal of respect for Aria. Due to her skills, Aria often relies on Fuuma to gather information thus giving them a bit of an info broker relationship. Aria often pays her in food for her work, much to her delight and further admiration.
Though Fuuma shows a great deal of respect and refers everyone with the honorific "-sama," she holds Akari in a very high regard compared to her other peers. Perhaps out of fear (or awe) of the potential lethality of the Mamiya technique or respect that her bloodline is of a Shinobi, Fuuma is willing to cooperate with Akari no matter how hard the task at hand may be.