If I run this flooring through my kitchen, which is a concrete slab, should I run it under the refrigerator and dishwasher?

Yes, run the flooring under the appliances to prevent future removal problems.

It will depend on how closely you can get the edge of this flooring to your fridge/dishwasher. If you can pull the fridge and dishwasher out and install this flooring underneath, I would recommend it, but it's not entirely necessary.