webRequest API not capturing all page requests from application - google-chrome

Question

I am trying to download JSON data from a web application. The URL/API is static and I can use it to call the webpage that returns the data. There is a session variable parameter that needs to be added to the URL/API call to connect to the server and download the JSON data which is created when you launch the application, but times out if the application is not actively used. My current process is to open the developer tools, launch the web application and when the specific JSON request is made I copy the parameter value then add it to a script that mimics the page request and downloads the JSON data.
I am trying to avoid manually copying and pasting this session variable parameter. I want to be able to automatically capture the web request, parse out the value that I need, set a cookie on my machine and then pick up the cookie by a php script to initiate the JSON data download with the valid session value.
I have looked into creating an extension in chrome using the chrome.webRequest.onResponseStarted with the following code:
chrome.webRequest.onCompleted.addListener(function(details) {
console.log(details);
chrome.cookies.set(
{ url: "http://localhost/MySite/", name: "MyCookie", value: "Tested" }
);
}, {urls:["<all_urls>"]} );
This code works for the main web requests but it doesn’t pick up all the JSON data requests that are made by the application. The application is swf format which is most likely the problem, but I can see the requests in the Network Panel tab of the Developer Tools and they are captured using chrome://net-internals which that leads me to believe that I should be able to capture them somehow.
I have looked into chrome.devtools.network but I cannot seem to figure out how that is supposed to work. Any advice or direction would be greatly appreciated.