heroku-buildpack-runit | Run multiple processes in a Heroku dyno | Platform As A Service library

On Heroku you don't get to pick the port you use. You must use the port Heroku assigns to you via the PORT environment variable. You also don't need Nginx to run Flask. Simply use gunicorn or another WSGI web server.

From the documentation (emphasis added):

Web servers

Outside of Heroku, web apps are sometimes executed inside a web server container. For example, PHP apps might run as a module inside Apache HTTPD, or Java apps might run inside Tomcat.

On Heroku, apps are completely self-contained and do not rely on runtime injection of a webserver into the execution environment to create a web-facing service. Each web process simply binds to a port, and listens for requests coming in on that port. The port to bind to is assigned by Heroku as the PORT environment variable.

This is typically implemented by using dependency declaration to add a webserver library to the app, such as Tornado for Python, Unicorn for Ruby, or Jetty for Java and other JVM-based languages. This happens entirely in user space, that is, within the app’s code. The contract with Heroku is for the process to bind to a port to serve requests. Heroku’s routers are then responsible for directing HTTP requests to the process on the right port.

One easy way to use the environment variable if it exists is to do something like this: