Regardless of how you attempt to make it only accessible from your Flash application, a determined user will certainly be able to view the page also. It can be as simple as proxying the requests through an HTTP proxy like Charles, Firebug or Wireshark.
There are things that can be done to make it more difficult to figure out what the data is from viewing the page directly. For instance, you can encrypt the data or output it as binary. But since SWF is an open sourced format, users can use decompilers or just inspect the ABC (Actionscript Byte Code) to see what is really going on.
The short answer is NO, you cannot protect the information available to the client side (Flash) from being accessible from other clients.