I don't believe there is the equivalent of an ASP.NET page master in Flex, but I have solved a similar problem by having a main flex object as a kind of manager object that doesn't do much except hold screen area and sort out the responses to user actions. So conceptually the manager looks something like
where the actual text contents of the various bits (together with image urls, link destinations for menu items etc) are held in one or more XML settings files.
Now, the issues with this are that you can end up with (in the extreme) just one page, which then handles everything in one Flex app, but on the other hand most of your content is in separate files accessed through URLRequest or similar. Also, and related, your load time may be longer, so it's quite cool to put in a custom preloader. I'm very used to creating objects dynamically so it doesn't bother me to start the page with almost nothing and create it as I go, but if you are more familiar with putting most things in <mx:...> declarations there is something of a culture shift to go through.
It does give you a very nice consistent feel across the whole, and means that you can get the structure right and then concentrate on the presentation content more.
Right now I can't give you a specific link to look at (one project is under commercial wraps, and another which I do have freedom to talk about isn't quite ready!) but if you're interested let me know and I'll see what I can do in a day or so...
Hope that helps,
I am new to the Flex world and am trying to create a master page and then reuse it in other susequent content pages. I read your above post and was wondering if you could direct me in the right direction.
Thanks for your help in advance.