For testing and development, staying with heroku is fine. However, for the production version of the site, scaling needs to be easy and cheap. For this reason, the code base will need to be able to run on a more scalable platform. I'm heavily considering AWS for this, but am open to suggestions.
I manage the AWS setup for a django app at my company so I could help with this. Scaling django on aws ec2, s3, etc has been pretty painless, but I don't know how this all works with a flask app though.
For testing and development, staying with heroku is fine. However, for the production version of the site, scaling needs to be easy and cheap. For this reason, the code base will need to be able to run on a more scalable platform. I'm heavily considering AWS for this, but am open to suggestions.