The Unicorn is a one-time character that only appeared in Hear Today, Gone Tomorrow.
It appears in Hear Today, Gone Tomorrow, when Flippy dreams about riding on it. When Fliqpy is chasing them with a helicopter, the unicorn ran faster and grew a pair of wings before jumping off a cliff. But Flippy and the unicorn died when Fliqpy killed them because of the blades of his helicopter, causing Flippy to wake up. It also later appears when Fliqpy imagines Lumpy being Flippy, riding on the unicorn and happily waving hello to him.