There are a few ways to get around this, up to a point.
Flash and accessiblity are opposite sides of the coin in most cases, however...
Check out the Flash accessibility tools, which allow embeddable information to be included with your movie(s) which search engines and, to a far lesser extent, text readers can cope with.
You can also use an external text file to hold the text that your Flash movie displays. This can be forced (up to that point I mentioned at the beginning of the post) to be read by search engines.
Much though I hate to admit it, about the best way to render fully accessible websites is to ditch Flash entirely. The second best is to put a lot of extra time, thought and effort into your Flash work which can go a long way to allowing accessible Flash content to be produced.
Try these links:
The last one has some really nice tips and tricks - well worth the read, but only you can answer whether or not it will be worth the effort.
Keep in mind that different browsers and screenreaders work in different ways and what may seem an idela solution for one setup may not work at al for others.
Test, test and test again.
My own recommendation is to lose the Flash intro movie. I've only ever seen one that actually added any value at all to the site it was on, and being as it was a showcase for the Flash animator whose website I was looking at...
Remove the Flash and put some nice, fully searchable/readable text on there with parhaps an image or two. Job done ;o)