First, you upgrade the source of FlaskBB using a simple

$ git pull

after that, the dependencies of FlaskBB should be updated (do not forget to switch into the virtualenv where you have installed FlaskBB into)

pip install --upgrade -r requirements.txt

If the database models changed after a release, you have to run the upgrade command:

$ flaskbb db upgrade

Don't forget to restart your application server when you are done upgrading!