When Peeta is awakened, he is startled, meaning that he was in a deep state of unconsciousness. As he regained consciousness, his eyes were working on focusing, trying to make sense of the visual stimulus changing from blank (eyes closed) to busy (eyes open). Fluttering eyelids here are a sign that the conscious mind has not yet taken control of the eyelid motor function; fluttering eyelids are indicated by rapid, almost spasming movement.
"Peeta, Peeta, wake up," I say in a soft, singsong voice. His eyelids flutter open and then he jumps...
(Collins, Catching Fire, Google Books)
People can deliberately flutter their eyelashes, and that action is a stereotyped female motion, meant to appear alluring. In this context, it was likely simply a symptom of Peeta going from unconscious to awake, and has no deeper meaning in the text. When in deep sleep, the eyelids often flutter during REM (rapid-eye movement) sleep, indicating dreaming; REM during a doze is sometimes indicated for the vague shapes seen during sleep paralysis.
it means they open gracefully and quickly like a butterfly's wings.