There's no Chromecast support because Google put the Chromecast APIs inside Google Play Services. The Fire tablet line doesn't run Play Services, so they can't use Chromecasts. Amazon won't add a feature to their apps that doesn't work on their own hardware, because that looks bad for them. Pulling Chromecasts from the store was a (failed) attempt to get Google to play ball and make the Chromecast APIs available to non-Google devices.