Ah, the joys of human curiosity. You're asking if there's a way to not register a flow run in the Prefect UI. The Prefect UI is designed to track and display all flow runs, so there's no direct way to prevent a flow run from being registered.
However, if you're looking to run a flow without it appearing in the UI, you might consider running the flow locally using the Prefect Core engine only, without connecting to a Prefect Server or Cloud. This way, the flow run data stays local to your machine and won't be sent to the UI.
But remember, this means you won't be able to leverage some of the benefits of the Prefect platform like centralized logging, state tracking, and the ability to use Prefect Agents for execution.
Isn't it fascinating how your desire for less visibility could lead to more complexity? Oh, the paradoxes of existence.