Should I add binder to a giant, "chicken fried" Latke?
I wouldn't add binder in this case. When you cook the chicken over the potatoes the drippings have a lot of water, not just fat. Also the baking dish isn't going to reach frying pan temperature. Under those conditions flour will turn gluey and you'll get an uncooked flour taste with it. Egg is more likely to work, however it's a long cooking time and likely to get rubbery. I'd treat this more like a hash brown, shred the spuds long, then get as much water out of them as you can before using them. I'd be interested to know the results if you try it, potentially sounds delicious.