I just don't like that spelling, at all. Honestly, though I tend to be a traditional spelling type of gal... Chloe is MUCH nicer IMO....
I like Chloe, but I almost always go fo the more classic spelling of names. I also think of Cs as softer & Ks as harder and harsher ( with a few exceptions like Kira & Kaya which I do like)
Other names you might like-
Not a fan of alternative spellings but this one doesn't bother me as much. Probably because I am so used to seeing it thanks to its famous name sake.
Chloe is much prettier. Khloe is a Kardashian sibling and will just lead to spelling errors.
Also, if you don't really talk to your friend and you're in love with Chloe, I'd just name her that. All worries aside.
TBH I'm not a big fan of the name either way, but if I had to pick, I would pick Khloe. I don't know why but Chloe has always seemed really whiny and disgusting to me. And now looking at it more closely, it's a lot like the word cholera. Maybe you'd like Claudia/Klaudia?
Love this name but hate the spelling. Chloe on the other hand is gorgeous.