Why Chloe Ann and not Chloe Anna?
I would choose Anna Chloe as Anna is one of my favourite names ever. I do like Chloe too, though, very pretty. A lovely combination.
I actually think Anna Chloe flows better too. Because with Chloe Ann, as the first name ends with a vowel and so does the beginning of the next name you have to be careful they don't run into one another as you say them - like Chloeyann.