first of all: there is no correct way to develop games ...
one advice I'd like to give you is: do not use CS4 for developement ... CS4 is a great tool to create graphics and animations, etc., but is terrible for programming ...
if you want to develop a proper game (or any sort of web app), that you don't want to scrap within months, you need to layout an extensible, flexible and robust architecture, which can only be done with rock solid code, and than plug in all you nice graphics and effects (which can be made in CS4 of course) ...
Flex is probably the fastest way to get UIs up and running ... if you are for example creating a strategy game, which requires a lot of forms and overviews etc., then you should use Flex for that, altough ASwing and other frameworks are reasonable alternatives ... I do not like Flex for a number of reasons, but I guess in the end they're all a matter of taste, so it is up to you to decide what you'll use to create all the standard UI your game will need to have ... the more UI to create, the more I'd advise you to use Flex ...
when it comes to servers, most people tend to use Red5 and SmartFox, which both perform quite well, yet in my opinion have quite a lot of unnecessary overhead and impose a lot on your networking engine ... still, you can start with them, and might find out they're just what you need ...
here comes my personal advice: use haXe ... it allows you to use one language for servers and clients ... also, it is a great language, once you get the hang of it ... I used AS2 and AS3 for a lot of time, but since I finally had the courage to switch to haXe, I don't want to go back ever again ... although the languages appear to be similar, they are not, so do not expect them to ... once you got your head around it, you'll understand what I mean ... check out ThreadRemotingServer for creating servers easily ... check out haxelib (more info here) to get some helpful stuff ... and don't be shy to post on the mailing list ... haXe has a great, friendly, helpful and enthusiastic community ... there's also a forum (which is not used so much) and an IRC channel to get support ...
hope this helps ... ;)