These are not flowers. These are pink colored pieces of paper – fortunes – tied on metal wires and arranged to resemble cherry blossoms.
At Heian Jingu, shown here, and at other shrines and temples it is popular to pull a fortune. The fortunes (O-mikuji) are usually taken from a series of 100 prophetic poems written in the Heian era (10th century), and generally have 7 or as many as 12 levels of luck/misfortune. If you get a fortune of bad luck, it is customary to tie it to a tree at the shrine, so the bad luck does not come home with you.