Handling multiple requests in Flask
Solution 1:
Yes, deploy your application on a different WSGI server, see the Flask deployment options documentation.
The server component that comes with Flask is really only meant for when you are developing your application; even though it can be configured to handle concurrent requests with app.run(threaded=True)
(as of Flask 1.0 this is the default). The above document lists several options for servers that can handle concurrent requests and are far more robust and tuneable.
Solution 2:
For requests that take a long time, you might want to consider starting a background job for them.