Greetings. I've got 8.1 running on ChromeOS Flex running on a Dell laptop. The main trick is that you need to enable the Linux Developer Environment, then load JRE from the "penguin" command line. You'll then download the Linux version of the client launcher from your gateway and unpack it to the "Linux Files" directory, where it will then be available in your Linux user home directory. The rest of the necessary steps are nearly the same for a standard Linux install, and are covered in this forum thread:
Once I've done this a few times, I plan to document all of these steps in one place and post them here and in that thread.
Hope this is helpful.
Cheers!
Paul