Hayes tapped home on 21 minutes after Craig Samson could only parry Calvin Zola's shot, with Flood capping off a dream Dons debut with a second-half header.
Substitute Kris Boyd pulled a goal back for Kilmarnock when he drilled home from 15 yards but Aberdeen held on to get their Scottish Premiership campaign off to a winning start.
Derek McInnes' side dominated possession in the opening exchanges but failed to make an early breakthrough, a tame effort from Zola the best they could muster.
But Aberdeen continued to press and they were rewarded when Hayes found himself perfectly positioned to net after Samson saved Zola's shot, the midfielder firing home his first goal since last December.
Kilmarnock's best chance of the half came from a deflected Gary Fisher free-kick, while Samson ensured just one goal separated the sides at the interval when he made a smart stop from Niall McGinn's backheel.
Aberdeen doubled their advantage early in the second half when Hayes turned provider for Flood, the Irishman heading his cross past Samson at the near post.
Kilmarnock were handed a lifeline when Boyd netted within minutes of his introduction. Rory McKenzie drove into the box and cut the ball back for the former Scotland striker, who made no mistake with a low shot.
Killie pushed for an equaliser in the closing stages, with Boyd shaving the post, but Aberdeen held on for a morale-boosting win.