The Evening Standard reports that Kate, 31, was on a royal engagement in London where she took a ride on a Routemaster and told a commuter: "My grandfather flew planes. I've had a few lessons on fixed wing."
Her late grandfather Peter Middleton was a Royal Air Force pilot and her parents worked for British Airways.
According to the Daily Mail, Kensington Palace would not confirm if Kate was being taught by her brother-in-law and Apache helicopter commander Prince Harry.
Kate was joined by Prince William on Thursday to promote the London Poppy Appeal.
Browse our gallery below to find out which celebs won't be taking flying lessons any time soon...
10 celebrities with a fear of flying
Duchess Kate reveals she's taking flying lessons
Although she says her fear of flying has improved over time, a traumatic experience left Jennifer afraid of taking to the skies for years. Speaking to China Daily recently, she said: "I had one really bad flight where we were caught in an electrical storm. We shouldn't have been in the air... What scares me is taking off, because I don't understand how the plane gets up there. I've heard all about the aerodynamics, the speed, the engine. Of course, when your number's up, it's up. Maybe I'm just a control freak..."
This Atomic Kitten developed a severe fear of flying around 10 years ago, when the band was at the height of its fame. In an interview about her phobia with the Mirror, she said: "I haven’t been on an aeroplane for four years, or on holiday for the past three years, and it’s all down to my chronic fear of flying. I have tried everything to combat it, from hypnotherapy to medication, and I’ve also been on four ‘fear of flying’ courses."
He may play the hard man in his movies, but flying gets this tough guy's knees knocking. Colin told contactmusic.com: "I hate it, man. It just seems highly unnatural to me. I've taken a few (pills) in my time. I'm trying not to (now) 'cause I've had a few messy affairs on planes. I've been lucky they haven't leaked a few (stories) of when I went bonkers. They nearly had the handcuffs out at one stage on British Airways."
Spiderman actress Kirsten has found a novel way of keeping her fear of flying at bay. She told Med India: "I always get scared on planes. Whenever I fly I pack those Bose headphones that dull the noise of the plane. I always wear them on take-off and landing".
Ben Affleck explained to Jay Leno how his fear first came about on The Tonight Show. When he was nine years old, he went on a flight to Washington by himself. It was struck by lightning and the engine caught fire. The night before, he had randomly seen a TV programme about child molesters. "It scared the lights out of me," he said. As the plane was coming in for an emergency landing, the man sitting next to him turned and said: "You know, if we land, they'll put us in a hotel. Don't worry - you can stay with me." The experience has stayed with him.
"I'm a really horrible flyer. I'm not superstitious about anything; I'm pretty much a realist, but flying, I kiss the plane. I'm petrified. It could be classified a phobia," Hollywood star Jennifer told contactmusic.com. For the first 10 minutes of any flight I'm sort of waiting for that sound that, for me - in my fantasy - it's like there's a nut that's come loose and it's going to go into the engine."
Brit actor Sean is another on-screen tough guy whose nemesis is flying. "My parents were afraid of flying and it rubbed off on me," he told contactmusic.com. "I used to drive to all my film locations in Europe but I couldn't when it came to filming The Lord Of The Rings in New Zealand. I wouldn't get into a helicopter with the rest of the cast. They had to wait for me to walk up the mountain and join them before they could start filming."
In an interview on Piers Morgan Tonight, Whoopi talked in depth about her long-standing hatred of jet-setting. She explained that her fear was instilled nearly 30 years ago when she witnessed a mid-air collision in San Diego. "I'm a visualist. So if I see it, it lives in my brain. So I always see it." She tackled her fears with a Virgin Atlantic course that helps individuals work through issues surrounding fear of flying. According to CNN, she added: "Some people are meant to fly. And I don't know if I was meant to fly, but I do it now."
Singing superstar Aretha Franklin's fear developed literally overnight. In February 1984, she cancelled two shows in Kansas City and then rescheduled her entire tour because she suddenly couldn't board a plane. In an interview with Glamour magazine, Franklin once revealed: "I turned down two singing opportunities in my career because of a fear of flying: one for the Queen of England and one at the pyramids."
Megan's solution to her flying phobia? Britney Spears. She told Perez Hilton: "I developed that (a fear of flying) when I turned 20... I had to come up with a way to deal with it because I didn’t want to have panic attacks every time I get on a plane. I know for a fact it’s not in my destiny to die listening to a Britney Spears album, so I always put that on in my (headphones) when I’m flying because I know it won't crash if I’ve got Britney on." Whatever works for you…