Only active animation is when they get attacked by land units. When a unit with an Anti Aircraft (AA) rating successfully shoots down an enemy aircraft, a missile streaks up and the attacking plane blows up. If you are doing the bombing a box pops up saying that your bomber was shot down by enemy flak.
IIRC, four flak units is the max that can be effective.
I didn't believe in Flak until recently. I was enduring a horrible air blitz from one AI until I stuffed my cities full of Flak. The odd bomber still got through but most died sooner rather than later.