In Django I always felt like I had to do things the Django way. In Flask I always felt like I was doing things the Python way.
- Using something that's not a database (e.g. ElasticSearch) and where you prefer speed over ACIDity also sucks because you probably don't want to use an ORM.
- Django's stubbornly-rigid MVC model sucks for building reactive web apps.
- If your structure is an API back-end that serves up JSON, and static JavaScript front-end that makes API calls to access data as needed, with appropriate API call restrictions, caching, and so forth, Flask is much more suited to this task. Doing this in Django just feels like you're swimming upstream the whole way. Django's ORM is also inefficient if you're dealing with a lot of data and only want to serve a small subset of it.
Yes, there have been improvements on all of these fronts with various Django projects, but a lot of the time Flask just gets the job done easier without the bloat.
But as for non-relational databases or other external systems, Django does not help you nor hinder you in any way. If you want to connect to, say, Redis - the code would look the same under Django and under Flask. You simply don't use the ORM for those things, since it's irrelevant. You use the appropriate client library for connecting to the external system.