Kaname Madoka
Kyoko's relationship with Madoka is barely mentioned. Kyoko pretty much leaves her alone after making a deal with Homura, as long as Kyoko leaves Madoka alone she can attack Sayaka as much as she wants. However this upsets Madoka. The two reach an understanding later when they try to save Sayaka together. I think these two would more or less get along if the circumstances where different. Kyoko would tease her a lot.
Miki Sayaka
Sayaka has the most dealing with Kyoko as Kyoko is trying to kill her for Mami's territory. At first they fight to the death, leave Madoka alone as per Homura's request. It changes after Sayaka starts to lose herself. And when she becomes a witch Kyoko and Madoka try to save her. The girls are losing and Homura comes in and save Madoka per Kyoko's request. Kyoko then tells Sayaka that she doesn't have to be alone anymore and that she will always stay with her. The two die shortly after. These two actually get along with each other, I think. They both made their wishes for someone else and want to protect everyone.
Akemi Homura
Kyoko and Homura have an understanding with each other. As long as Kyoko leaves Madoka alone there is no problem and these two get along with each other. They will fight along side each other when needed or listen to the other if it sounds like a good plan, like getting Madoka out.
Tomoe Mami
Kyoko respects Mami, as she doesn't come in until after Mami is dead. But it shows that she repects her strength. I think these two would have gotten along just fine had they been allowed too. Since Mami dies before Kyoko arrives there is no interaction between them.
Kyubey
Kyoko is more or less okay with Kyubey until she finds out the truth about the magical girls. It just tears her up. She then hates Kyubey and works with Madoka to save Sayaka. Kyubey is there but Kyoko wants nothing to do with him anymore. I think given the chance she would kill him just as Homura did.