About the phrase "I'm gonna lick me a rainbow."
I watched Shrek Forever After, 2010 movie. There is a scene where Shrek is carrying a cake on which a rainbow and an ogre face were painted at Shrek's kids' party. Then, Donkey shows up and says, "I'm gonna lick me a rainbow." before he licks the cake. Why is 'me' added before a rainbow? It doesn't sound natural.
And I found out there is goods with the phrase printed on it, such as T-shirts and mugs. That's why I was more curious.

Question

Answer

You are right. In the sentence, "I'm gonna lick me a rainbow", the 'me' should not be there.

However, you will often hear people add the 'me' because it sounds cute and funny. It emphasizes that you're doing something in a playful way.

Examples:
   I'm gonna get me some cookies. --> I am going to get some cookies.
   I'm gonna buy me a new car. --> I am going to buy (myself) a new car.

OVERALL: The 'me' is wrong grammatically but common in spoken English as a joke.

Answer

Some people think it sounds funny to use bad grammar. It's a poor attempt at humor.