DeployGate is not available to install from the Amazon Appstore at this moment.
However, there are two ways to download DeployGate directly:
If you use a Distribution Page
You can use the DeployGate Distribution Page 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: