Then they need a CC license for the same version of ID and they can sync the fonts. They need the same version of ID you are using and so typekit access is moot.
Ben from Typekit here. Our license doesn't allow you to send the font files to the printer. They would either need their own Typekit account so they can sync the fonts or they would need the font installed on their machine.
However, exporting a PDF will embed the fonts into the PDF which you can send to the printer. I would make sure the PDF is rendering as expected before sending but this should work for you and won't require the printer to install/sync the same fonts.
Let me know if you have any further questions.
When I'm ready to send my PDF and files over to the printer, they ask that I include the font files.
Ummmm... Unless I'm seriously out of touch, the fonts should be embedded in the PDF so there is no need to send them. Has the printer said why they need these fonts?
Thanks everybody. They wanted the files so that they could make some changes and add the FSC logo to the project. You've answered my question, cheers.
The place to make those changes is in ID, not the PDF....