How to secure a REST Api on flask
You should use token based authentication technique to secure your API, the concept is simple once your user signs in, your site should save it somewhere and you send back that token to your user.
For each call to your API, user should send token with every API request and you should validate the encoded toke and either deny or send back the response.
Have a look here: https://realpython.com/blog/python/token-based-authentication-with-flask/
Check this too http://flask-jwt-extended.readthedocs.io/en/latest/
For better performance, you can store your session tokens in a NOSQL database like Redis.
To support logins with social media sites, you should use OAuth which is working in the same way except it send back a couple of more tokens to the client.