Your macOS system includes a security feature, called Gatekeeper, that can block the installation of applications downloaded from sources other than the Mac App Store or from a list of “identified developers”. This is to prevent you from installing “malware” – malicious software on your Mac.
1-You may want to re-download the app.
2-It is known that sometimes macOS gives this error mistakenly. Sometimes installing some trusted apps may be prevented. You may want to simply restart your Mac. And further, on your Mac, go to System Preferences > Software Update and check to see if there is an update available.
Hope it works! BTW if you want to save Amazon Music on you PC after your Amazon Prime expires, you can use Amazon Music Converter to download Amazon Music songs into several universal audio formats then save on your PC.