Flex applications are, like Flash applications, compiled into an SWF file. Once a user visits the webpage containing your Flex application, the SWF file is downloaded to and run from the client computer. Instead of a seperate session each user receives their own copy of your Flex application. The client computer runs the Flash VM, which in turn fires up the local copy of your Flex application.
Furthermore, Flex uses the Actionscript scripting language. The current version is Actionscript 3. Actionscript 3 is single-threaded. By now you probably already see where this is going. The single-threaded nature of Flex applications means synchronization is not required.