Can I / Should I use WordPress as a CMS for my Flash application

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:

• http://www.kirupa.com/developer/actionscript/displayinphp.htm
• http://www.techmynd.com/get-data-in-flash-from-php/
• http://www.dreamincode.net/forums/topic/9848-pass-complex-data-from-php-to-flash/
• http://www.video-animation.com/dbase001.shtml
• http://www.smartwebby.com/Flash/external_data.asp
• http://www.devx.com/webdev/Article/36748

Of course then there is what Adobe has:

• http://www.google.com/search?q=php+flash+data+site:adobe.com

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.)