Sharepoint - Get Check-out Documents using Javascript

I can suggest 3 ways to achieve this:

First 2 are REST and Javascript:

You could use SP.File.checkOutType property to determine whether document is checked out of a document library

REST

$.ajax({url: "/_api/web/getFileByServerRelativeUrl('" + docUrl  + "')/checkOutType",
        headers: { "Accept": "application/json; odata=verbose" }, 
        success: function(data) {
                  if(data.d.CheckOutType == 0) {
                        console.log('The file is checked out');
                  }
               }
});

CSOM (JavaScript)

var context = SP.ClientContext.get_current();
var web = context.get_web();
var file = web.getFileByServerRelativeUrl(docUrl);
context.load(file);

context.executeQueryAsync(
     function(){
         if(file.get_checkOutType() == SP.CheckOutType.online) {
                        console.log('The file is checked out');
         }    
      },
      function(sender, args){    
          console.log(args.get_message());
      }
);

Third one is the easiest based on Spservices:

SpServices

Use SpServices GetListItems and write a query where you search for all the items where "CheckOutType"("checkedOutTo" please check the internal name) is not null. You can then iterate through all the items.

Do let me know if you need help writing the query. Cheers!