A person that does research on SEO will certainly stumble upon articles saying that flash can be bad for SEO. This statement is certainly true in most cases than not.
The number one reason that flash is bad for SEO is simply because everything is in a single .swf file. Although the .swf file may have different pages, everything is still held inside a single page and search engines do not treat # as an extra page. In addition to that, search engines will certainly have a problem crawling in a flash site if it is not professionally and cleanly coded.
There has also been a surge in the number of smart phone users. A good example is the iPhone. The browser in the iPhone does not support flash and there is little chance that it will in the future as well. A flash site will be absolutely useless for a smart phone user and in return, the site itself will lose potential visitors as well.
Flash sites are also known to give bad user experience. These sites take longer to load as compared with a site that uses HTML. In addition to that, flash is also known to cause problem to legacy computers as they account for a significant amount of resources.
However, flash can be good for entertainment purposes. Take gaming for example, Runescape is powered by Flash and there are millions of its users as well. A lot of the games in Facebook use flash as well. But bear in mind that these type of sites or applications can stand on its own with little amount of SEO. For many other sites that do need SEO to get noticed, stay clear from flash.