The royal couple came face-to-beak with Zephyr, a 4-year-old bald eagle, and were happily chatting to his handler when the bird suddenly flapped his wings, catching them by surprise.
The prince said he wasn't going to hold the bird, which is the mascot for a squadron of the Army Air Corps, because he has done so before – and knows what he can do!
Charles, 66, and Camilla, 68, met Zephyr last year during the famed flower show.
"It was less dramatic than the pictures suggest," a spokesman at his office at Clarence House tells PEOPLE.
When it comes to animal encounters, Charles and Camilla were more at ease at a dog show last month at Scotland's Dumfries House. They royals are proud owners of two Jack Russell rescues, Beth and Bluebell.
After their amusing incident with Zephr, The couple continued to walk around the grounds of the show. Camilla bought four cheese scones and picked up a soft toy version of the British film and TV character Shaun the Sheep, revealing she is something of a fan.
Why Prince Charles and Camilla Parker Bowles Are the Most Fun Royal Couple
"He's adorable isn't he?" she said. "I have to watch it all the time with the grandchildren – it's their favorite film. Fortunately, I rather like it too."
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