wave [intransitive, transitive] to move your hand or arm from side to side in the air in order to attract attention, say hello, etc.
The people on the bus waved and we waved back.
wave at/to somebody Why did you wave at him?
He waved to the crowd as they greeted him.
wave something The driver leaped out, waving his fist and swearing.
wave something about/around A man in the water was shouting and waving his arms around frantically.
wave something at somebody She waved her hand dismissively at the housekeeper.
wave somebody something My mother was crying as I waved her goodbye.
wave something to somebody My mother was crying as I waved goodbye to her.
flick [transitive] flick something + adv./prep. to hit something lightly with a sudden quick movement, especially using your finger and thumb together, or your hand
She flicked the dust off her collar.
The horse was flicking flies away with its tail.
James flicked a peanut at her.
Please don't flick ash on the carpet!
The striker flicked the ball into the back of the net.
She snatched up her briefcase and flicked it open.
This is the action that a child often does. That is after washing his hands, he may wave his soaked hands at someone's face just for fun, and that makes many drops of water land on that person's face.
How would you express that action in English?
He waved his soaked hands at my face for fun
He flicked the water from his soaked hands onto my face for fun?