The Burke family was flying out of JFK Airport to Las Vegas earlier this month when things got heated. According to Cameron Burke -- who shot video of the incident -- he and his family had the cake as carry-on. It was special ordered to celebrate his wife's 40th.

The Burkes say a flight attendant first argued with them over whether to place it in overhead or under the seat ... and then another attendant arrived and said it couldn't be on board at all. Cameron says that 2nd attendant, the "mean" one told him he was being "non-compliant" when he attempted to calm things down.

He admits he asked her, "Have you been drinking?" -- because he felt she was being erratic and irrational about a cake. In the video, you can see the Burke kids getting upset ... especially when police showed up.

Officers escorted the Burkes, who went peacefully, off the plane. A JetBlue spokesman told ABC7 -- which first reported the story -- the Burkes were yelling and cursing at the crew, and disruptive.

Cameron denies that, and says he's already talking to attorneys about filing a lawsuit.