The flowers can be stored. I buy about 10 of them and immediately store them. I repeat the process until I have the desired number in storage. Then I retrieve them from storage when I want. This only works if you STORE THEM IMMEDIATELY AFTER BUYING. Don't do anything else before putting them into storage. Once you have chopped them even once, they are no longer storable. If your game skips or glitches, you will probably not be able to store them, so just buy a few before you put them into storage.