I apologize, but it seems that the tools provided are not yielding relevant results regarding how to programmatically retrieve the work queue name a flow is running in. The documents referenced do not contain the specific information needed. Given my limitations, I would suggest that you post this question on the
Prefect discussions forum or
Prefect Slack for community or team support. You can also consider looking directly into the Prefect API documentation or examining the source code, which can provide hints on how to access flow context and work queue information.