Now that "Activity" is gone from Safari, how do I find and download a streaming flv file on a Mac? Is there a plugin (for any browser) anyone can recommend? An app? 

It seems like all browsers got rid of this easy resource tracking feature (Chrome too).
You can see still browse resources in the web inspector.



To download a file, you can copy the URL from the right sidebar, paste it on the location bar, and press ⌥↩.

The web inspector can be shown by pressing ⌥⌘I if you've enabled showing the develop menu in the advanced preferences.