I sometimes build applications in Flash for the web that need a fair bit of dynamic data. Would WordPress be a good fit for my CMS solution? can it "talk" to flash? Does it allow output as different formats such as XML, JSON, or AMF?
Absolutely. WordPress is implemented in PHP and anything Flash needed to interface with can be coded as a plugin, probably very easily. You can also implement any embedding of Flash as ShortCodes.
Here are some (honestly not very good) links on the subject of PHP & Flash:
Of course then there is what Adobe has:
Can you update your question to provide more details on exactly what you need for/from Flash? Maybe included some links that explain the things you want WordPress handling for Flash (Flash is quite a large beast, you know.)
In re: XML, remember too that WordPress has (even without a plugin) a very nice XML-RPC interface.
Yes, but it's going to involve a lot of work to get it to send the right information in the right format. You might look into this plugin that puts the information out in JSON: