The first place to start is by determining if Flex's built-in Resource Bundles are what you need. Of course their examples all show binding to a bunch of resource manager calls. This isn't the most elegant way of doing things, but if it works for you, go for it.
Or you can simply build a Proxy that reads an XML file, that has all the resources inside it. See the ApplicationSkeleton demo for an idea of how you can make it work this way.
http://trac.puremvc.org/Demo_AS3_Flex_AppSkeletonThat demo has one config file that is read, and it has a setting that tells it the approprate xml file for the language. (there is only an 'en' defined).
So if your app has lots of labels, you might want to put it into separate files.
If it's relatively small and you want users to be able to change languages without fetching another file, you might put all labels for all supported languages inside a single xml file that's loaded.
-=Cliff>