Have you tried to call her again?
I am confused by this
"She does not warn or ask if it is a convenient time - and it wasn't but she took offence that after 15 mins or so I ended the chat."
She took offense it wasnt a convenient time but still chatted for 15 min?
You also say you dont click.
Would you be friends with this person if she wasnt your cousin?
I wouldn't say you are estranged - unless you had an established relationship before and then stopped talking
It seems to be a case of not having enough in common (apart from dna) or your cousin not interested in a relationship with you