The traditional list
January is carnation and snowdrop. February is violet and primrose. March is daffodil. April is daisy and sweet pea. May is lily of the valley and hawthorn. June is rose and honeysuckle.
July is larkspur and water lily. August is gladiolus and poppy. September is aster and morning glory. October is marigold and cosmos. November is chrysanthemum. December is narcissus and holly.
Not every birth month flower is easy to find as a cut flower, and some lists differ. Ask the florist what they can get. Even one stem of the birth flower tucked into a bouquet is a nice detail. See birthday flowers.