Not all varieties flowers and other varieties don't flower every year.

If the tops are dying then you have to harvest the potatoes or the ones in the ground will start to grow new plants. (Don't bother to ask me how I know.)

Your potatoes look like they could be left to die back more than that. Those look like they are still growing and could perhaps use some more fertilizer. You can carefully feel down in the soil with your hands to find out how the tubers are developing. Then decide, let them grow some more or harvest now.