Typekit desktop fonts are installed on your system to be available in any app, as long as it works with system fonts. Fireworks should work just fine.
There are a couple things you need to sync all desktop fonts from Typekit:
- The Creative Cloud app
- A Creative Cloud subscription
- A Typekit subscription, the Portfolio Plan if you want access to all desktop fonts
I hope this helps. Let me know if you have any further questions.