Can flask rest api application can run on gunicorn alone?
Flask - logic to respond to HTTP request
gunicorn - Helps manage concurrency for these HTTP requests, logging, worker timeouts
nginx - scalability and protection. If the load for your application is higher, Nginx would help for load balancing without crashing your Application Server, helps to serve static content if any

So if load for your application is less and no static content to serve, in my opinion, flask + gunicorn should be OK.
I'm currently developing HTTP Rest API server using Flask. I don't have any static media, and all url are being served by @app.route pattern in Flask Framework. Can Flask run on Gunicorn alone with out webserver?