In June of 2011, Adobe announced they were ceasing support for Adobe AIR™ on Linux.
YNAB and many other popular packages (Pandora, Tweetdeck) run on the AIR platform. While all versions of YNAB 3 will run on Linux, we can't promise permanent compatibility for all future development.
The YNAB license allows installation on as many computers and operating systems as you need (for your personal/household use). Hopefully this gives you more options should you find it's not running smoothly on Linux.
These instructions should work for most versions of Linux (but not all). Please make sure the trial runs on your system before purchasing.