Your sentence is mostly clear and understandable, but here is a slightly improved version with corrected grammar and punctuation to make it even better:
"Sheep don’t live in the savannah. The savannah is home to pink flamingos catching shrimp, striped zebras running around, and big elephants spraying water from their trunks."
Actually, your original sentence is correct! The grammar and punctuation are fine, and the sentence is easy to understand. Good job!
Just remember that the word savannah is spelled with two n's. Also, it's great that you used commas to separate the animals in the list.