I never liked the idea of running Flash inside the web browser, but a single file .swf game format is almost as good as any ROM game dump.
Some games didn't mind running locally from an .swf file, but some others had a "URL protection", presumably to prevent people from embedding their flash games at other websites, and they didn't make an exception for localhost.
Long time ago I've fixed hundreds of such flash games using RABCDAsm and made them work in standalone Flash Player.
Took a brief look at Flashpoint Archive, it seems their way to fix URL check is to spin up a web server to present an address the game expects.
when archiving, it's preferable to leave the files in the state you originally found them
As a bit of background, flash games were often sponsored. The bigger websites would pay hundreds to thousands of dollars to put their (clickable) logo in the beginning of a game, and sometimes would also have either timed or permanent exclusivity to their website.