I don't know if she is one of Kim's closest friends in life but on the tour, Daniela is close to Kim. Daniela said in an interview around New Haven time, that She and Kim have been frineds since they were 14 playing in tournaments in europe together and know each other very well. and get along well. Also they practice together I a bit I think, well I know they definately did at US Open, Leipzig, Zurich together were photograohed together in Toronto so are together a bit. Also Kim watched Dani's matches in Stanford and I think San Diego when Dani was really struggling, she went to support Dani.
Now I could be wrong but I remember from a poll on here that Kim had a friend called Veerle (spelling ?) maybe she is one of Kim's closest friends.
I think she is close with Jen, I remember reading an article, now ofcourse this doesn't mean it is true
but in it it said Kim had said Jen was her closest friend on tour, which I find believable given there are so many photos of them together and that they practice a lot together. As for after there match in LA I'd ignore it Jen was upset she lost as is understandable
Now if only they'd play double together
I think she and Ai are close to. Maybe Kim gave Ai that present on Kim's bday cause they also won Roland garros doubles that day
I think she is also good friends with Kirsten Flipkens
And also Kristof Vleigen I remember Kim rang him the night before he played the final in Adelaide this year and wished him luck so they must be friends.