Is your app truly a desktop application? if its a kiosk? Are you actually using the flash player or the AIR runtime?
Flash can be a RAM beast, depending on how long your run it for. Everything that is on the screen at once will need to be loaded into ram, so you will wanna think about that as you get the machine. Hopefully, with good memory management, you can keep it tidy so you don't have to worry about runaways.
Processor.. well thats always helpful :) But I don't have any specific specs on flash vs processor's.. I can tell you as of 9.0.115.0 the player can support multi-core, hardware accelerated full screen video. I am guessing your kiosk will be running in full screen mode so you will wanna take advantage of that. At a max of 4 CPU's, this will help flash in all kinda ways.
I would be looking at a GOOD video card... a good one.. not the crazy card that will set you back your life savings. We aren't talking real time hardware accelerated 3d :) but it should help give your fullscreen app a boost.
Here are some of the details on 9.0.115 that would wanna pay attention too, under improved performance.
http://www.adobe.com/support/documentation/en/flashplayer/9/releasenotes.ht...
:) hope this is useful!
-ross