It's possible! And for the most part it works well. I hate that this this is so complicated but I'm gonna go ahead and post my setup ayway.
The native Vive controller support in flyinside is not good for this because
A) you can only turn dials in one direction (It's better to use head cursor with right menu button as interact)
B) You can not control the rudders or yoke with the Vive controllers (I explain how to do this in step 2)
Step 1.
Disable the Vive controller support in flyinside.
To disable Vive controllers in flyinside unfortunately I found no way to do this other than exploiting the bug that
when you're using a steam controller skin the Vive controllers get disabled in flyinside.
So try using various steam controller skins until the Vive controllers no longer show up in flyinside.
Step 2.
Map the Vive controller as a gamepad
In order to map the flyinside and xplane keys to the Vive controllers you need to install a program called steamvr_wheel.
https://github.com/mdovgialo/steam-vr-wheel
There's a batch file called steam-vr-gamepad.bat
I use that one. Just run it before you run flyinside.
Step 3.
Map the keys!
Now your Vive controllers is seen as a gamepad in flysinside and Xplane.
Just map all the keys you need in both flyinside and xplane.
right menu button: flysinside's interact key (works well for controlling the cockpit).
left menu button: recenter
left touchpad: throttle/rudder
right touchpad: pitch/roll
and so on...
Sorry that this is so complicated but once you do it a few times it's not bad and actually worth it.
I should mention that when you play like this, you won't actually "see" the Vive controllers. But you can still reach around in the cockpit while using the interact button which feels pretty good