As of July 2013 there's a Flask template on Azure.

Start with that. Clone it to your computer. There's some IIS stuff at the root, and a hello world Flask in the folder FlaskApplication. You can test the Flask app on your computer python __init__.py. I don't know how to test the IIS site locally.
I don't know how dependencies work either. There's a Pip requirements.txt in the template, and also the source trees of Flask and a couple of other libraries.
I copied an app of mine from Heroku to Azure. Got it working eventually. The biggest difficulty was finding and reading logs (you need to turn on all the logging in the IIS manager, then browse to an FTP site, then the logs are deep in some weird named xml file), which made the two minor problems take longer than they should to solve
- Working directory is different to Heroku (at the IIS site root, rather than the Flask site root)
- The template has a dodgy
web.config that silently deletes query strings from get requests
This was the problem
<action type="Rewrite" url="handler.fcgi/{R:1}" appendQueryString="false" />