No, you do not!
You can use the full capabilities of Flowsana, including its rules and all other workflows, from its own web portal at https://flowsana.net, with any Asana subscription level.*
The only element of Flowsana that requires an Asana Business or Enterprise subscription is to use Flowsana rule actions directly incorporated into Asana rules via the Asana rule builder. That's not any limitation of Flowsana, but is because third-party rule actions are only accessible in Asana's rule builder via custom rules, and custom rules are only available at the Asana Business and Enterprise subscription levels.
* There are some limitations at the Basic/Free Asana subscription level, due to its limited feature set.