A pratical way is to get ViWizard Amazon Music Converter, which is available for both Windows and Mac computer. It is a robust music downloader and converter for help you in saving songs from Amazon Music to FLAC, AAC, M4A, WAV, and more popular audio formats.
Step 1 Select Amazon Songs to download
Step 2 Set FLAC as the Output Format
Step 3 Convert Amazon Music to FLAC