If you're an Adobe Creative Cloud member then you gain free access to BC and Typkit. You still need embed Typekit script into the header and configure your typkit "Kit". there is no built-in component in BC for typekit as I know of.
Right. That was not the question, so this is not the answer. I have no idea why it's flagged as "Correct," because I sure didn't do it.
Let me restate it: I have a Typekit kit for a site and the code is embedded in the header. It does not show up on the BC site. Similar kits show up fine on non-BC sites, such as Wordpress and straight HTML. Is there a reason for this?
I had the same issue a while back. Check the typekit settings, i.e the URL it's poiting to. is it a trial version? can you provide a URL?
Also, if this a secure site (e-commerce) then the script URL should start with HTTPS not HTTP.