I clicked on Launch Servers, the servers are ready and the remote application is running, but the JMeter GUI doesn’t open

The remote application requires your approval for connecting to the load servers, due to Amazon’s security standards. There is probably an open dialog box waiting for your approval:

Minimize all open windows , or use Ctrl+Alt to look for that open pop-up. Once approved the JMeter application will open and you can continue with your test.