In a small 1-quart sauce pan, combine 1/2 cup of the white sugar and 1/2 cup water. Add the jamaica and bring to a boil, stirring constantly to dissolve. Simmer for about 10 minutes. Pour the syrup through a strainer and discard the Jamaica flowers.
Turn on the oven to 350 degrees. Melt 6 tablespoons the butter in a 10-inch skillet (preferably non-stick) and sprinkle brown sugar over and the simple syrup. Sprinkle in the rhubarb and simmer until nearly cooked, about 5 minutes.
In another large bowl, whisk together the flours, salt, and baking powder and baking soda. In the bowl of a stand mixer add the remaining 6 tablespoons butter and remaining 1 1/4 cup white sugar. Beat until light and fluffy. Add the vanilla, egg and 1 cup of the sour cream. Once combined, add the flour in 3 additions until just combined. Scrape down the sides of the bowl.
Pour the batter evenly over the fruit in the skillet. Slide the skillet into the oven and bake 25 to 30 minutes, until the cake is golden brown and springy to the touch at the center. Remove and let cool 10 minutes.
While the cake is cooling make the sweetened sour cream. Whisk together the remaining 1 cup of sour cream and sifted powdered sugar.
Invert a plate over the skillet, then, holding plate and skillet firmly together with towels or pot holders, invert the two in one swift movement. Remove the skillet and the cake is ready to serve. It’s best right out of the oven.