Securely saving AZURE_STORAGE_KEY and storage account name in Linux systems
Instead of storing them as variables in the bash script themselves, can you store them as environment variables on the system from which the bash script is executing? This is a pretty common practice that will allow your scripts to execute on different systems without having to modify the script on each and every one. 

Not sure what you mean by the AWS cli "saves the key and the secret in encrypted format", but if you look at the credentials file in ~/.aws, your access key and secret access key are both in plain text. I'm not sure how the Azure cli manages profiles, but AWS uses the AWS_PROFILE environment variable to distinguish which account the cli should execute as.