Problem installing Google Chrome to Phone
(BTW, I also can't find it on the
  Google Market)


If you cannot find an application in the Market, this means the application is not compatible with your device. AppBrain cannot install applications that you cannot find from the Market, since in the AppBrain installation, you are brought to the Market to install your application (AppBrain is application discovery service, not alternative Market). 

Are you possibly using Android 2.1, which does not have the Cloud-to-Device Messaging API, and therefore cannot use Chrome to Phone? Or possibly you have multiple phones linked to your AppBrain account?