The key is that the Flash runtime will look onto the host (server) that you are attempting to read data from (assuming it is not the host from which you just loaded the flanis.swf file) and if it can find a special "crossdomain.xml" file which contains a reference back to the host where the FlAniS is run from, then it will allow access to read the data.
So, you do need to have access (or cooperation) from the host where the data resides. Without that, there is no way to read the data. Assuming that you do have htat, here is what you need to do:
Flash provides many ways to restrict this access. For example, you can explicitly name the domains to allow access from: instead of "*" as the value for the "domain" attribute, you might have:
Complete documentation about the form of this file and the tags and their attributes can be found here
You or your site administrators might also find this article of interest, as it deals with the issue of cross-domain scripting and cross-site request forgery.