<p>As a web developer, a number of the projects I work on fall under government umbrellas and hence are subject to 508 Accessibility laws, and sometimes W3C accessibility guidelines. To what extent can Flash be used while still meeting these requirements?</p>

<p>For using javascript, the mantra is "Degrade gracefully" by providing the same content and function, just on different pages, or in a less interactive/dynamic way. This allows non-javascript browsers/users still use the site, as well as allowing search engine bots to access all of the content. Users of screen reading software, such as JAWS and Orca also are still able to fully use the site.</p>

<p>With flash, is there a similar way to gracefully fall back for non-flash users? If not, how accessible is flash-based content to search engine bots? And also, how do screen readers handle flash-based content?</p>

I'm visually impaired to the point where I use magnification tools and TTS for convenience but not as a necessity. I can tell you that Flash just doesn't work with the majority of accessibility tools out there.  I believe JAWS (the market leader for Windows but not overwhelmingly dominant by any means) says it has Flash support, but most Flash developers don't seem to put in the work necessary to allow JAWS to grok the textual content of the Flash movie.  And many visually impaired users just don't even have flash installed because for 95%+ of the time it's simply useless to them.
Another consideration is that the built-in Text-to-speech that Mac OS X provides also can't do anything with most Flash movies.
IMO 'degrading' or offering a link to an HTML version of your content is probably the only practical means of ensuring your site is accessible.  If you are starting from scratch I would strongly consider JavaScript / JQuery over Flash if at all possible.