OK, you don't grow potatoes for the flowers. However, they're a good indicator of plant maturity, and their blossoming announces that there are new potatoes to be had in exchange for a little digging.
I planted them early this year, since they were already sprouting. With an eye to the weather forecast for the following few weeks, they went out in March when there were no air frosts (3°C or less) predicted. Forecasts that are three weeks ahead are subject to change, so I kept an eye on things, ready to cover any emerging sprouts with a tarpaulin whenever the frosts are forecast for that night. By March any frosts lasting all day are probably over, so the tarpaulin approach will likely keep the plants alive. A nasty cold snap, if it happens, could finish them off, so there is a risk involved.
I dug up the first potatoes yesterday. Delicious.
Potatoes grown from tubers are clones of the parent plant. New varieties are bred from seeds, but if you try this approach, be aware that the fruits are poisonous.