We don't have one to test with yet. If any Vive Wireless owner could comment, that would be great That said, I'm assuming it's designed to work with just about anything SteamVR, and I'd be surprised if it has issues with FlyInside.
Turns out the problem is not unique to FlyInside. Many of my other VR games are no longer working, including steam games. They don't like the fact that the VR video and monitor video are not plugged into the same graphics card. Of course, the Vive wireless adapter has its own video card. There are indication that my video card arrangement may be the problem. I was already planning to upgrade my video card. So after that happens next week I'll let you know if the problem still exists.
Replaced my video card and now Flyinside works flawlessly with my Vive wireless adapter. I think the problem may have had something to do with my SLI setup.