Once you get the Blimp after Snow Mountain, Step 16, you can fly to the south-western island to find “Romeo and Juliet”. Juliet is sick. Romeo ask you to look for a Red Flower.
Fly to the south-eastern island and meet the stranded Dr. Einst. In exchange for a Scrap 7, he'll tell you where to find the Red Flower. Equip Scrap 7 and talk to him again.
If you haven't found a Scrap 7, the mouse in the Rococo Sewers sells them for 1500 GP.
One Red Flower grows right behind the house, under the left tree. Go pick it up and bring it to Romeo. Equip the Red Flower and talk to him. He'll reward you with 300 GP.