not sure whats out there specifically for flash stuff but you could use google webmaster tools to check your sites SEO
First up and foremost I would like to commend you to your great effort in setting up this site !!! and especially with such controversial subject like SEO.
I have been reading through some of it, but not quiet all as yet and I find it extremely interesting, but at first glance I did not see anything in regards to using Flex compiler SEO ??? and / or Html SEO ?
Now I would be very interested to find out a little more in detail what you are looking for here:
**** Can anyone suggest automated accessibility / seo testing tools that I can use to validate my website? *****
My personal answer to your question above and as it stand is YES & NO !
Yes because I do have an Application which could maybe suite your idea of SEO in one way or the other. It is operating on different web sites at the moment covering five (5) continents with around 190 feedback channels using six (6) different movements, but Analyzing is just a part of that what it was developed to do.
The App. has been tested every day for several times since early Dec. 2010 and has proven extremely responsive and effective to each of the web sites SEOs it is used with, but as said before I need to know a little more to see if this really could be of any help to you !