Use Reflector to mirror my desktop to an Apple TV or Chromecast
Unfortunately, this is not possible. Reflector 4 is designed to screen mirror/cast an iOS or Android device to your Mac or Windows PC. Reflector 4 can only receive AirPlay and Cast connections, but cannot send them to AirPlay/Cast receivers such as Apple TV and Google Chromecast devices. These are limitations that Reflector 4 is bound to.
There is a way to accomplish this by using the combination of Reflector 4 and AirParrot 3.