What is the proper format for the flag service calls? I'm running Drupal 7 with the Services 3 and the Flag Service modules installed. I'm having trouble trying to figure out how to format the the call in REST format.  Can someone provide a short example?
The flag service module (and probably the others you've listed in your comments) define their resources as actions, so you access them at a URL like:  

http://server/[endpoint]/[module]/[action].json.


So for the flag action provided by the flag module that would be something like:

http://server/endpoint/flag/flag.json


This little snippet works well for me, based on a REST server with no authentication turned on and an endpoint with the path 'api':

$url = 'http://server-name/api/flag/flag.json';

$args = array(
  'flag_name' =&gt; 'bookmarks',
  'content_id' =&gt; 8,
  'action' =&gt; 'flag',
  'uid' =&gt; 1,

  // You wouldn't normally want this, the flag module provides it as an override 
  // but it's a security risk. With proper authentication you can safely remove it.
  // I'm just using it for testing.
  'skip_permission_check' =&gt; 1 
);

// Perform the curl
$curl = curl_init();
curl_setopt($curl, CURLOPT_URL, $url);
curl_setopt($curl, CURLOPT_HTTPHEADER, array('Content-Type: application/json'));
curl_setopt($curl, CURLOPT_POST, 1); 
curl_setopt($curl, CURLOPT_POSTFIELDS, json_encode($args));
curl_setopt($curl, CURLOPT_RETURNTRANSFER, TRUE);

$response = curl_exec($curl);

$http_code = curl_getinfo($curl, CURLINFO_HTTP_CODE);

curl_close($curl);

if ($http_code == 200) {
  // Success
}


Answering the original question (What is the proper format for the flag service calls?), it's simply a matter of calling the correct URL and POSTing the required arguments to it, from whatever programming language you might be using.