Cannot find Direct Tv Stream app on my Chromecast with Google TV [white model]

You have to side load it. Dtv Stream app is not available in the google play store on devices running android tv.

If you cannot find the app most likely they do not offer it as an app on your TV.  Your best bet would be to buy an external device such as a Directv Stream Box/Roku/Fire Stick.  My recommendation for an external device is the Directv Stream Box it has a better user experience than what the other devices offer!

I already told OP Dtv stream app is not available on android tv devices. Chromecast with google tv runs android tv. You can sideload it, though.