Rare Flowers are found in only a few regions on the Ark. The are used in a few of the Rockwell Recipes. Collecting a decent number of these can be quite the challenge.
Finding Rare Flowers is a simple matter. You just need to harvest bushes and you'll get the odd Rare Flower as a rare drop. But only certain bushes in certain regions have any chance of providing Rare Flowers as a drop. And your best method of harvesting is by hand.
The bushes that drop rare flowers are found on the top of mountains and in the swamps. So that means you'll have to head either to the mountain tops or into the swamps. Both provide challenges and dangers, so make sure you are prepared before you head out.
If you have a flyer you may be able to zip up to the top of a mountain, harvest some Rare Flowers and get out before you end up in too much trouble. Be careful.
The screenshots below show the bushes where I have found Rare Flowers. The first two screenshots are of bushes in the Swamps, while the third one is of some bushes on the tops of a mountain.
The fastest method of harvesting Rare Flowers is with Dino Power. Regardless of where you are going to harvest, a good berry harvesting Dino is your best buddy for getting Rare Flowers fast and in quantity.
A Trike will do the Trick, but a Stego or bigger is definitely better. I find when harvesting berries, seeds, and rare flowers that it's all in the tail. How big is it? How large an area does it clear? And definitely how much Melee Damage does that Dino have?
In the screenshots below I show harvesting with a Stego which is an earlier tame and an easier to acquire Dino. These were taken just inside the edge of the Swamp along the East Coast of the main Ark island. Map GPS Coordinates are 56.3 - 83.3.