You raise some fair points. That being said, the narrative doesn't treat her actions as justified. Sumika refuses Kanoko's request to abolish the schwester system in no uncertain terms and was planning to do the opposite by making schwesterships permanent. In fact, both Sumika and Hime want Kanoko to make an effort to get along better with Mitsuki(who, despite her jealousy, tries to keep things civil between them).
I'm not so sure that Kanoko doesn't even care about Hime. Her anger toward Mitsuki isn't solely based in jealousy, but because Mitsuki's love confession caused Hime anguish due to her being unable to return Mitsuki's feelings, which is probably part of the reason why Kanoko hasn't confessed. She even tries to convince Hime to stay at the salon, whereas it would probably have been easier to let her go; Kanoko could still see her at school, whereas Mitsuki, who goes to a different school, would probably never see Hime again.
Considering the warnings Kanoko received about the consequences her jealousy might have, I personally think that Kanoko's going to eventually face some backlash as a result of her feelings for Hime and her jealousy of Mitsuki coming to light, since Hime only has an inkling of the latter and no idea of the former, and the fallout will probably make the drama between Hime and Mitsuki in Volume 7 seem tame. This will probably lead to her relationships with Hime, Sumika and Mitsuki changing, although it's too soon to say how.
In short, I'm not denying her flaws, but I still believe she can change for the better.
Kanoko wasn't mad at Mitsuki because Hime was unable to return Mitsuki's feelings, but because Hime wasn't able to reset like she usually does when someone confesses to her. Kanoko was mad because Hime had to take her seriously, unlike most people who confess to Hime. She sees Yano as a threat.
Look, I fully expect Kanoko to have a redemption arc of some kind down the line, but I think from everything we've had from her perspective she's never once taken the time to think about how anyone else feels. Even in the latest chapters she keeps thinking that Hime and Sumika are acting strange, and she means not how she wants them to act like. She is sorely lacking in empathy.
It's not about flaws. Like I said last time, it's not the jealousy that's the problem, it's the lack of self-reflection. That goes beyond a flaw to a personality defect.