How Do I Control the Directv Streaming App (installed on my TV) Using My Voice Through Chromecast TV (the dongle)

You can't.  If you want Voice Control, install the app on the Chromecast.

Thanks for your input @JefferMC. @TVisthegreatest, the voice control feature with Chromecast TV only allows you to open or close the DIRECTV app. The full voice control functionality only works with the Gemini and Gemini Air devices. For more help, visit Chromecast support or the Google TV support center. John, DIRECTV Community Team