American Goldfinch; they have beaks well suited to plucking petals to get to the seeds. And they will perch on flowers to get at them. They're attracted to neighborhood bird feeders, preferring thistle seed, but have developed a taste for many annual flower seeds as well, including your zinnias.  Bird-netting can be used but is messy to work with and can trap birds.  They are nesting now and feed their young seed (usually thistle) that is partially digested by the parents.