In order to add a map to a page you need to create an html element you can target with jQuery and include the map compare JS & CSS files. Once the element exists in the DOM you can add a map by targetting it with jQuery and calling the mapCompare jQuery function created by the map compare JS file.
The mapCompare function takes an object as its parameter. This object needs one key, config which points to either a string or another object. If it points to a string then the string needs to be a reference to a json config file. If security requirements won't let you host flat files then you can use a javascript object -- which just needs to be the contents of the existing config files.
$('#EXAMPLE-SELECTOR').mapCompare({config: 'CONFIG-FILE.json'});