This script will loop through layers in the first two layer groups in a photoshop file toggling them one by one and exporting a png of each flattened combination

PS-SavePairsOfLayers.jsx

// This script will loop through layers in the first two layer groups
// in a photoshop file toggling them one by one and exporting a png of
// each flattened combination

// NOTE: Start the file with all the grouped layers set invisible, 
// but the groups themselves visible, and any non-grouped layets you want 
// to put in all the files visible.

#target photoshop

var MyGroups = app.activeDocument.layerSets;  
var filePath="~/Desktop/"; //Change this to where you want to output the files to go

//Loop through group 1
var i; 
for(i = 0; i < MyGroups[0].layers.length; i++) { 
  //Set which group 1 layer we're working with 
  var obj = MyGroups[0].layers[i];
  
  //turn this layer on 
  obj.visible=true;  
  
  //Loop through group 2
  var j;
  for(j = 0; j < MyGroups[1].layers.length; j++) { 
    //set which layer in group 2 we're working with 
    var objinner = MyGroups[1].layers[j];  
    //turn this layer on 
    objinner.visible = true; 
    //Save file 
    var fileName = obj.name + "-" + objinner.name; 
    var fileNamePath = filePath + fileName+".png";
    SavePNG(fileNamePath);  
    
    //turn this layer off 
    objinner.visible = false;  
    //Next! 
  }  
  //turn off our group 1 layer 
  obj.visible=false; 
} 

function SavePNG(saveFile){ 
  var pngOpts = new ExportOptionsSaveForWeb; 
  pngOpts.format = SaveDocumentType.PNG; 
  pngOpts.PNG8 = false;  
  pngOpts.transparency = true;  
  pngOpts.interlaced = false;  
  pngOpts.quality = 100; 
  activeDocument.exportDocument(new File(saveFile),ExportType.SAVEFORWEB,pngOpts);  
}