Are there any plant species that grow only in the Feywild? (Trees, shrubs, flowers, etc.)
Information about both the Feywild (from the 4th and 5th editions) and its predecessor, the plane of Faerie, is suitable.
Related question: Where can I find more lore about fey and eladrin?
As far as I can tell, no named plant species are stated as native (uniquely or non-uniquely) to the Feywild in 5th Edition material. But, we have an example of a plant that is unique to the Feywild, though its name is not given.
In Ghosts of Saltmarsh, there is a hull upgrade available to ships called Living Vessel:
This vessel’s hull was crafted in the Feywild under the direction of master eladrin shipwrights. It is a living plant, drawing sustenance from water and sunlight. Vines covered in thick leaves hang over its side, and the wood runs with fresh sap when damaged. The ship gains a +2 bonus to all Constitution checks or saving throws. As long as the ship has at least 1 hit point, it regains 10 hit points every minute.
The ship itself is a plant that is native to the Feywild, so whatever plant this ship upgrade is made from is an example of what you're looking for.
Additionally, Ben-Ben has noted some plans in 4th Edition material:
Something can be found in the Player's Option: Heroes of the Feywild (4e, PO:HotF). This book is not tied to a specific Prime world, but these ideas, I think, can be used in everyone's campaign. Not everything from the list is probably unique to the Feywild (given in the section “Feywild Gear”), but it has unique properties.
Feywine Grapes ("Feywine Raisin", PO:HotF, p. 134):
Raisins made from these grapes, when thrown into a glass of water, instantly ferment and create wine.
Flower of the Dawn (PO:HotF, p. 134)
This rare flower emits a fragrance that instantly awakens a sleeping creature, even one in an enchanted slumber.
Flowers of the Summer Queen’s Gown (PO:HotF, p. 134)
Where the Summer Queen walks, summer flowers bloom. Such a flower blooms eternal in the Feywild. Where their seeds are thrown (even in the tundra), flowers bloom for one day.
Senaliesse Chrysanthemum (PO:HotF, p. 135)
Chrysanthemums from the forest near the Summer Queen's domain may be gifted by fey to mark them as friends of the fey. Gnomes, nymphs and pixies refrain from mischiefs on those who wear such a flower. The flower retains its appearance until the bearer leaves the Feywild.
Star-indigo plant (PO:HotF, p. 135)
This plant grows only in the wild fields of the Feywild. In daylight, its flowers are not much different from ordinary wildflowers, but at dusk its flowers glow faintly, and at night they glow as brightly as the stars. Dyes made from this plant pass glowing quality to clothing and ink. The light from an object colored with these dyes is like the light from a candle.
