If a local agent is running connected to a remote prefect server, and prefect ui shows the agent is indeed active, what could be the reason for a late flow when using "quick run"?

In my experience, it's usually due to label mismatch between the flow/flow run and the agent.

I've seen late runs often occurring due to label mismatch too, but let us know if you are facing a different issue.

Ah, thank you. However, I have not set any labels at all. Should I set a consistent label for the flows and agent?

You can do that, but make sure that labels for agent are superset of labels on the flow. You can see an example here.