I am doing initial design work for the back end of a site that will use mainly Flash for the front end. I am not a Flash dev myself, and I don't care about general comments for or against Flash. What I want to know is:
What is the current state of the art in communicating with the server to use dynamic content? Is AJAX an option? What other techniques are preferred, for example fetching remote XML? Json? Are there caveats? Can anyone point me to best practices guides?
There are many different ways, including all of the ones you already mentioned. Of course, your choices will depend on what language you use for the back-end.
Have a look at AMF, ActionScript's own transfer protocol. The protocol is available for most larger server platforms, including Adobe's own BlazeDS (Java), as well as plenty of 3rd party solutions that range in maturity. See the following links for more info:
http://theflashblog.com/?p=414
http://en.wikipedia.org/wiki/Action_Message_Format