The Red Flower is what the animals call fire, something humans can create and they cannot: "No creature in the Jungle will call fire by its proper name. Every beast lives in deadly fear of it, and invents a hundred ways of describing it" (1.90). And because the animals cannot create or control it, they are scared of it. Fire, then, represents power and difference, as well as fear.
Bagheera sends Mowgli to retrieve fire from the village in order to intimidate Shere Khan. When Mowgli does, he sees himself in the fire: "This thing will die if I do not give it things to eat" (1.105), he observes. Mowgli is like the fire in more ways than he realizes. Like fire, he also is something that the animals, especially cowardly Shere Khan, cannot create or control. And because they don't understand Mowgli either, they fear him, and would rather cast him out than have him live so close to him, where he could burn them (figuratively) at any time.