For years, no search engine spiders could read Flash websites.
Today, Google can read Flash websites:
Note the last sentence in bold.
In addition, while Google can read Flash-based websites I doubt that any other search engine can read Flash-based websites.
One other suggestion that Google provides that I thought was useful:
You could also consider using sIFR (Scalable Inman Flash Replacement). sIFR (an open-source project) lets webmasters replace text elements with Flash equivalents. Using this technique, content and navigation is displayed by an embedded Flash object but, because the content is contained in the HTML source, it can be read by non-Flash users (including search engines).