This solution works for me, on Kali Linux, using my keyboard; as always, YMMV.

In Burp Suite Pro:

  • Select Project Options from the tabs along the top
  • Select the Sessions tab
  • Scroll down to Cookie Jar
  • Click "Open cookie jar"
  • Ctrl+A to select the entire contents
  • Ctrl+C to copy all of those content

Now go to a file open in your favourite text editor. For me this is a file open in vim within a the gnome terminals Kali uses.

Ctrl+Shift+Insert to paste the contents of the clipboard into that file.

Now run this command, and you should have a list of cookie names you can work through:

grep <target domain> <name of file> | tr -d "/" | cut -f 3 | sort | uniq