Who is a person who grows or sells flowers?

A person who grows flowers (ornimental horticulture) is called a horticulturist; horticulture is divided into a number of divisions:

commercial horticulture

ornimental horticulture

retail horticulture

public space management

floriculture etc.

A person who sells flowers is normally called a florist, but may have a background in design or horticulture.