The Evil Flower is a rather useless and harmful plant for the most part. Being near it, picking it, or eating it will decrease your health and the petals you retrieve from it are nearly useless. However, collecting 10 of them and refining them will give you Nightmare Fuel. This would require you to give up quite a bit of sanity to accomplish though so it isn't necessarily recommended.
It is generally better to hold on to some Rabbits and perform some other action that will make you go insane until the rabbits turn into Beardlings. You can then murder them in your inventory which can possibly give you Nightmare Fuel. After that, you can do different things to increase your Sanity.
Because these aren't generally considered useful, they are best left alone. A ring of these is generally found around or in close proximity to the Things (the items needed to leave the world).
