Hah! "more like toes than fingers"...
So THAT's where "tater tots" come from!!
As for the potato plant flowers, they play no role at all in the formation of the spuds, just in the forming of seeds. I think most folks just use the flowers as a signal when you can begin to harvest the young, "new" potatoes. And of course some folks who like to grow new stock or new varieties collect the seed (known as TPS) and start their crop with those.
Shoe (who had country-fried taters with his stir-fried chicken and eggplant for supper tonight. *burp)