This is not how to make a flower clock like the one shown in the picture above, but is a rather more subtle way of using the flowers themselves to indicate the time. It is based upon the observation that particular plants open and close their petals at different times of the day. By planting the right varieties you can make an admittedly rather crude timepiece. I found this information on the Gardening Launch Pad website.

Make a Clock with Flowers Who needs a watch when you can tell time with flowers? No, you don’t need to wear a corsage on your wrist. If you plant a flower clock in your yard, you can look out the window and know the hour at almost any time of day.
The flower clock was developed by Carolus Linnaeus, a Swedish botanist. Linnaeus was a professor at the University of Uppsala, and in his studies he noticed that the flowers of different plants open and close at certain times each day. In 1748 he decided to plant a flower clock, and those who visited could look at it and tell what hour it was.
You could plant such a clock, too. First you’ll need to select some flowers that open and close at different times. Try to find plants that grow well in your area, ones that flower at the same time of year. Below is a list of popular plants whose blossoms open and close at specific hours.
What to Do: Make a small circle (about a foot to eighteen inches in diameter) in some outdoor soil. Plant the flowers in order around the outside of the circle so you can read them like a clock’s face. When they bloom, you’ll have your own flower clock. But get moving-your botanical clock is ticking!
*morning glories and wild roses open: 5:00-6:00 a.m.
*dandelions open: 7:00-8:00 a.m.
*African daisies open: 8:00-9:00 a.m.
*gentians open: 9:00-10:00 a.m.

See more at Gardening Launch Pad