Depending upon where you live and your shipping costs, it could be that you don't have to worry much about the seasonality of flowers. However, here is a brief guide by season, so that you can be aware of which flowers may require some research on their availability.

Spring flowers: daffodils, iris, lilacs, lilies, peonies, tulips.

Summer flowers: calla lilies, dahlias, daisies, hydrangea, geraniums.

Autumn flowers: chrysanthemums, marigolds, Shasta daisies, zinnias.

Flowers whose stock are not dramatically affected by season: carnations, gardenias, orchids, and roses.