The two heads of the Copy Flower provide an answer! The Copy Flower evidently reproduces through budding - and perhaps even vegetative propagation would be successful. While quite rare (and pricey!), once a interested gardener is able to obtain Copy Flower seeds and successfully sustain at least one plant, it's nearly trivial to acquire a whole flowerbed's worth.
Of course, because of the flower's reproductive method, any given flowerbed of them is highly susceptible to disease or fungal rot (unfortunately quite common in the Mushroom Kingdom). Once a pathogen is established in one flower, it will quickly spread and decimate the whole collection - which brings us back to their rarity and price!