It’s because the Flash gallery’s SWF (the Flash file) isn’t colour managed.

Flash does now support colour management.  But the SWF would have to be ActionScript3 (the version in Lightroom is AS2)

You also have to consider what the person viewing your site is using. Assuming the visitor isn’t using a Flash-hobbled device like an iPad, that computer would have to be running Flash Player 10 and would only get good colour if the monitor is properly colour-managed.

Alternatives:

• If you want to use a Flash-based gallery, look at SlideShowPro for Lightroom. It’s not colour-managed though.
• If you can code Flash, get SlideShowPro standalone
• Commission me to build a colour-managed Flash site