Correct spelling, explanation: shriek is an onomatopoeia, a word mimicking a sound, and is most likely based on an Old Germanic word schrichen. There are similar words spelled with ee or ea, but in this case, the old german origins explain the spelling of shriek.

Definition of shriek:
noun
1. a high-pitched cry
I fell asleep while watching a horror movie, and a shriek of a monster woke me up.
verb
1. to let out a high-pitched scream
I have two parrots and while they don’t want to talk, they shriek loudly whenever they see me.

Incorrect spelling, explanation: shreak is a spelling that would most likely fit the pronunciation and it’s incorrect mostly because of the origins of the word, which is most likely the old Germanic word schrichen. As you see, it has the i in the spelling, so while the long i sound can have many forms in writing, shriek should be spelled with the ie diphthong.