I have the same problem on both my laptop and desktop linked to the same Adobe CC account. I have lots of Web Fonts installed through Typekit but only like 4 to 6 of them appear in the fonts list. I've tried signing out of Adobe CC desktop application and restarting Muse, as this has worked in the past, but lately nothing seems to work. Any ideas?
Can you try quitting CC, Adobe Muse, and then restarting your computer? Launch applications and log in.
Let us know if that worked.
Please try reinstalling the Typekit fonts again, if is still doesn't work by the suggestions given by Preran.