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Also, you can have your 1-time-playing flash file on the home page, and make a separate flash file that acts as if it has already been played on the other pages (as far as I know, there is no other way, but I'm sure there is).
The search engines do not understand nor index flash well. Google is easily the best at indexing flash, and they still aren't that good at it. They will most likely find your links, but from personal experience I question whether or not the links they find within flash (similar to those they find within javascript) are actually transferred any PageRank.
Yahoo and MSN either don't (last time I did any research) index flash at all or are extremely bad at it meaning if your only navigation is flash, they won't even know about your other pages.
Finally, flash based navigation is simply not very user friendly. By having your navigation in flash you are alienating a percentage of your visitors right from the start.
Bottom line, Flash is a great adjunct to a site, but don't make it a requirement for your site to function properly.