I don't know anything about chainfire autoroot for the Nexus 7 as I used the Nexus Root Toolkit v2.1.4 by WugFresh that I mentioned earlier, although chainfire software is highly recommended for most things and I have used his software often on my galaxy phones and tablets. As long as you have a Nexus 7 (2013) you definitely need RAZOR-FLO. I stuck with android lollipop as v1.4 didn't work when I upgraded to marshmallow so I used RAZOR-FLO: Android 5.1.1 - Build: LMY48T.
I will take a chance on posting a link as it is nothing to do with forums or satellite so I am sure the mods and admin won't mind, for all Nexus software's go here and scroll down the page to your model number, but please please please make sure you choose your correct model:
If you need any more help I cannot get back online now until probably Monday evening.
Please Login or Register to see the links
If any mods don't like the link please delete and don't smack my hands as I am only trying to help.