Mix the first 3 ingredients for the batter together in a bowl. Whisk the egg whites until firm and fold into the batter.
Cut each courgette in 1/2 lengthways, but not cutting all the way through, so you still have the flower intact on the end. Heat oil for deep frying to 375 degrees F (190 degrees C). Dip each courgette with its flower into the batter, and fry in the oil until crispy and golden brown. Drain them on kitchen paper, then place them on a serving plate, sprinkle with salt, chiles and mint, and drizzle with vinegar.