I want to be my cousin's fiancee's best friend
Does she like you more than your cousin?
She wants to have a sleepover session with me when I was at her place.
It's great you want to be friends all around, but it's really suspicious that you want to get together before they are married. You need to hold off or you'd look like you want to get into a relationship and have him cheat.
She said she just wants to watch netflix and chill.
You realize that's a euphemism, right?  I definitely think this looks suspicious and in the interest of your cousin's happiness and your relationship with them I think you should cut off his fiance immediately.