First off if you're using BlazeDS and only going to have Flex clients, you should setup BlazeDS remote objects instead of REST service. You can use amf channels and send objects instead of xml/json/text.
That being said, What version of flex are you using? I have only done this with Flex 4 (and actionscript 3) using URLRequest and URLLoader (or with HTTPRequest)
Example:
var dataRequest:URLRequest;
var dataLoader:URLLoader;
dataRequest = new URLRequest("http://localhost:8080/Path/to/webservice");
//using post in this case, you can also acess GET
dataRequest.method = URLRequestMethod.POST;
var variables:URLVariables = new URLVariables();
variables.xmlCoords = xml;
dataRequest.data = variables;
dataRequest.contentType = "application/xml";
dataRequest.requestHeaders.push(new URLRequestHeader("accept", "application/xml"));
dataLoader.load(dataRequest);
Is it feasible to create a REST client with Flex? this topic has been discussed here with some good pointers and I think you should check it out.
Hopefully this can help you out some / point you in the right direction.