We have been able to use Typekit fonts within our web applications but the same references do not seem to work within our Cordova mobile application.
I have read that it is not possible because of the missing "referer" header. Is this still the case? If so, is there a workaround?
The font licensing does not allow you to include fonts from Typekit in any app that will be download and installed on iOS or Android. You would need to purchase a separate font license from the foundry which owns the font(s) to package them with your app.
Here's a link to the Typekit font licensing FAQ, for future reference:
We hope to be able to support embedded fonts in the future, but it isn't available at this time. Sorry I couldn't be of more help; please let me know if you have any other questions!