I believe you need to convert the cookies to the format that BAS understands, and then import them into BAS using a standard method.
Take a look:
https://chromedevtools.github.io/devtools-protocol/tot/Network/#type-Cookie
Maybe our problem is related with flash or something, see this thread http://community.bablosoft.com/topic/2321/twitter-users-to-tag-not-coming-up-in-browser/6