Security of python flask REST API using HTTP Basic Authentication
Your current system is (very!) insecure, the login information can be seen during transit by anyone.
The easiest way to add secure HTTP is to install a proxy server like nginx. Then nginx is configured for secure HTTP, but it relays all the requests to the Flask application listening on a private socket without encryption.
This link will send you to the nginx documentation on secure HTTP.
Alternatively, you can have HTTPS running directly from Flask. The link has clear instructions of how to do this. It is a quick, easy method to use while developing.
For production, I'd use Apache's mod_ssl function, or as already stated by Miguel, nginx, as proxy servers.