don't design website using flash, you won't get the benefits of SEO at its fullest potential.
flash is a complementary thing (used for things like banner, header etc) to a website design but don't design the complete site in flash.
Even I would recommend not to develop you site in complete flash it seems more attractive, but less importance you get in SEO. If you are creating your site in flash, but make sure the content should be in HTML for that at least you can utilize the benefit of inter linking for your inner pages.
Using flash in website doesn't harm SEO. Flash or Java plug-in contained content can be supplemented with text on the page. But never build your website completely in flash as search engines can not index any of the text content, or even the links.
As I said, Google can index your Flash website. It's harder to control what you get to the index, and indeed have control over the search engine visibility. Some other search engines may not be able to do that, but Yandex at least crawls Flash files.
It was around 2008 when Google indexed the pure Flash website of the ad agency I was working for. Wasn't expecting that.
I personally think Flash is terrible for modern web design. I mean, sure you could use it to make web games, but please don't ever, EVER use it to design a website. Use only pure HTML and CSS to design your website. Flash slows everything down and Google can't even crawl it so it's just useless.