Since I had nothing but time on my hands I reset got each month until I got the 3 flowers for that month and made a list!
January - Windflowers, Pansy, Mums
February - Pansy, Windflowers, Hyacinths
March - Tulips, Pansy, Hyacinths
April - Tulips, Windflowers, Hyacinth
May - Roses, Tulips, Windflowers
June - Lillies, Tulips, Cosmos
July - Roses, Lillies, Cosmos
August - Lillies, Cosmos, Mums
September - Cosmos, Lillies, Mums
October - Mums, Cosmos, Roses
November - Mums, Cosmos, Roses
December - Pansy, Mums, Roses
I doubled checked August and September since they had the same flowers but after double checking them, they do indeed have the same flowers. I’ve also found that while the months have 3 flowers that can be native, the 3 possible native flowers are not guaranteed to be available to be bought in the shop. I have 2 friends who have birthdays in October and neither of them had Roses in their shop but had flowers that weren’t native to October such as Hyacinths, Windflowers, and Pansies.