I had the same problem with 'Traffic360', everything worked fine with FSX, but with the Rift and FlyInside I didn't see the other planes.
I added the following line in the FSX_flyinside.cfg : "SimObjectPaths.x=SimObjects\JFTraffic360"
in the [Main]-section where the "x" stands for the following number, in my case the "x" is a "6"
I also added "SimObjectPaths.x=SimObjects\TrafficX" where the "x" in my case is a "7"
After saving and restarting FlyInside with the Rift I finally could see the other planes.
I hope it works for you as well.
You can find the FSX_flyinside.cfg file in here : "C:\Users\YOUR_USER\AppData\Roaming\Microsoft\FSX"