DeployGate is not available to install from the Amazon App Store at this moment.
However, there are two ways to download DeployGate directly:
If you use a Distribution Page
You can use our DeployGate Client application and the DeployGate Distribution Page (Link Distribution) to distribute your app. Find the "Click here if Google Play is not available" link. Click it to install both DeployGate and your app.
If you don't use the Distribution Page
You can get the DeployGate APK file from here:
By installing the APK file you downloaded to Fire Tablet, you can use DeployGate cliente application.