I've download numerous fonts from Typekit which synced perfectly to Indesign / Photoshop / Illustrator. (I am using Adobe CS6)
For some reason some of these fonts have no removed themselves. For example I had the whole family of FreightBig Pro and now only have 6 fonts showing in my applications.
In Creative Cloud it is telling me all fonts are downloaded and synced, but this is not the case.
I have tried turning Typekit on and off through preferences and logging in and out to ensure the right account is being used but nothing seems to be working..
Moving to type-kit.
I'm sorry that you are having trouble syncing fonts from Typekit. Please send some of the Creative Cloud sync log files from your computer to firstname.lastname@example.org, and we will look into it further.
Here are instructions on where to find the logs on OS X and Windows:
It would also help if you could include a screenshot of the Fonts tab in the Creative Cloud desktop application, similar to this: