for the FLASH side of things..
I dont think any of the flash builders will do or be as flexible as you want/may need them to be in this project.
I would shoot for straight Adobe FLASH...
as for which one.. I suppose that depends on the 'bridging' software you end up using.
I have never attempted this myself yet.. but skim articles on it when i see them.
I have seen more AS3 than AS2 (ActionScript) out there I believe.
Are you trying to use this FLASH GUI 'locally' on your machine?
(ie: you have the flash.swf on your desktop... and the Arduino connected to the same machine via USB/SERIAL?)
or you trying to add more into the mix by having this FLASH GUI be located on the 'internet' and accessible to anyone with a web connection?
Seems like the former, but I wanted to be clear.
That being said.. Im not well versed in AS3, but I can hold my own in AS2
Flash does not have a way to communicate to serial, databases, write files..etc...etc.. itself.. it always needs some 3rd party 'bridge' (server side script...something).. like PHP, ASP, CGI..etc... to take this 'data/info' FLASH is sending.. and do whatever it is you need done with it...
(in your case, you'd be sending out the data/info from your flash movie/app to some sort of 'handler', that in turn will support serial communication and output it for your Arduino that is waiting/listening for these serial commands/data)
Have you researched on any pre-existing Flash solutions for this?
You mention firmeta (firmata).. and I think AS3glue is another?
here is a link that be helpful:
I can help with the flash side of things, once you get that far.