Flaming Flower Stamens are obtained from fire flowers that you find in the wild.
They are spread around the map, and you may have seen plenty already. They emit a small glow, and are often surrounded by fire near the flower. Use Hydro elemental abilities to extinguish the fire so you can pick them up. You can use Barbara's elemental skill, and touch them with the water rings to easily extinguish them, or just use Barbara's normal attacks.
Flaming Flower Stamen Uses
Fire Flower Stamens are used for the fire related potions. Flaming Essential Oil increases your party's Pyro DMG by 25%, while Heatshield Potion increases your party's Pyro RES by 25%.
It will also be used to craft Warming Bottle, an item that will be available in Dragonspine to lower sheer cold status. You obtain the blueprint to craft these by getting your Frostbearing Tree to level 4. Since Sheer Cold will play an important part as you travel in Dragonspine, you might want to craft many of these to have an easier time.
Thousand Winds Temple
There are 2 flaming flowers very close to the Temple of the Wolf domain door, in Thousand Winds Temple.
Another 2 that you can easily pick up, it's close to the teleport waypoint in Cape Oath, which is just southeast of Thousand Winds Temple.
4 flaming flowers in one of the hilichurl camps. It's close to the tower that's at the end of the area shown above.
North of Jueyun Karst
Heading over to Liyue region, there are 3/4 north of Jueyun Karst. It's easier to get there by going to the teleport waypoint in Qingyun Peak if you've already unlocked it. Simple glide to the east to the marked area.
About 3 or 4 in each area marked above. They are quite easy to spot and reach. Teleport to the Statue of The Seven in Dunyu Ruins, and head to the 3 separate locations to pick up a lot of flaming flowers.
3 in Tianqiu Valley, not far from the teleport waypoint.
West of Jueyun Karst, is Nantianmen. There are 4 flaming flowers here, with a hidden treasure that you can also "dig" in the middle of the group of flowers.