With one of the Rares, invite some miis over to harvest the seeds. You need a seed that'll give you a regular breed, but with the stem/shape of a Rare. (Like all the wreath flowers in one of my pictures!) Then, grow that new flower (regular breed with Rare stem), and leave it on the workbench when you exit the game, so it saves it as your most recent flower. Now do a StreetPass with them!