Deploying updates to a Flask application
Looks like Docker might be my best bet:

Have Nginx running on the host, and the application running in container A with Gunicorn. Nginx directs traffic to container A.
Before starting the file sync, tear down container A and start up container B, which listens on the same local port. Container B can be a maintenance page or a copy of the application.
Start file sync and wait for it to finish. When done, tear down container B, and start container A again.
I'm looking for high-level insight here, as someone coming from the PHP ecosystem. What's the common way to deploy updates to a live Flask application thats running on a single server (no load balancing nodes), served by some WSGI like Gunicorn behind Nginx?
Specifically, when you pull updates from a git repository or rsync files to the server, I'm assuming this leaves a small window where a request can come through to the application while its files are changing.
I've mostly deployed Laravel applications for production, so to prevent this is use php artisan down to throw up a maintenance page while files copy, and php artisan up to bring the site back up when its all done.
What's the equivalent with Flask, or is there some other way of handling this (Nginx config)?
Thanks