You cannot pick flowers if there are not any blooming on the Scenes in your garden.
In order to make the flowers in your garden bloom, you will need to create Scenes that are set to "Public" view mode. This is effective for 5 days.
You also cannot pick flowers in other people's gardens if you do not have any Help Hearts, even if there are flowers blooming.
Help Hearts recover at a rate of 1 every 10 minutes. If you run out of hearts, trying visiting the garden again later.