Prince Charles held the two-year-old bird, Zephyr, as he and the Duchess of Cornwall came to the end of their tour of the show at the Queen's Norfolk retreat.
As he held the eagle, which weighs more than 10lbs, Zephyr flapped her wings and the Prince was almost clipped by her impressive four foot span.
Pleased to meet you: The Prince of Wales holds an eagle called Zephyr during a visit to the 132nd Sandringham Flower Show
Go on, make me a mascot: The eagle needs royal approval to become the official mascot of the Army Air Corps
Lisa Falco, from the Imperial Bird of Prey Academy in Billericay, Essex, said they hoped the encounter would further their cause to make Zephyr the official mascot of the Army Air Corps.
She said: 'We are awaiting royal approval so hopefully this meeting will help with that.'
Royal perch: Zephyr lands on the prince's arm
About 20,000 people attended the annual show and many braved heavy rain to offer their congratulations to the new grandparents.
Ann Whiting, of Castle Rising, Norfolk presented the couple with a crocheted shawl which she had spent six months making.
Prince Charles was heard saying the Duke and Duchess of Cambridge would be 'thrilled' with the gift.
Brolly good: The couple braved the wet weather to attend the Norfolk event
Brightening up their day: Well-wishers were happy to wait in the rain for a chance to meet the royals at Sandringham House
Meet and greet: Camilla shakes hands with the waiting public
The Sandringham Women's Institute member said: 'I started soon after the announcement that she was pregnant was made. I wanted to give them something special but which they could also use. He seemed pleased with it and said he would pass it on.'
Sheila Clarke, 55, travelled from Glasgow to hand over a teddy bear wearing a bib which she had embroidered with the name George.
The prince asked her: 'Did you place a bet on the sex and name?'
Granddad's: Charles said he would pass on toys to the Prince of Cambridge, but seems rather taken with this teddy himself
Gift for a prince: Another well-wisher passed on a personalised bear for the new royal baby
Pretty in pink: The prince stops to admire a baby girl as he chatted to the crowd
For you: Meanwhile the Duchess is presented with some seeds by 22-month-old Evelyn Holt
Puppy love: He also paused to stroke a dog
Say cheese! The dog loving duchess posed for a picture with Jack Russell, Scooby
Afterwards, she said: 'I told him a bought the bib a little while ago but waited until the birth to embroider the name on it. He seemed very happy with the present.'
Meanwhile, Evelyn Holt, 22 months old, presented Charles with some blue crocus bulbs as he told members of the public that his new grandson, George, was 'doing very well'.
Her mother, Victoria Holt, from Wymondham, Norfolk, said: 'He seemed very interested in Evelyn and gave her lots of attention.'
Afterwards, she said: 'I told him a bought the bib a little while ago but waited until the birth to embroider the name on it. He seemed very happy with the present.'
Meanwhile, Evelyn Holt, 22 months old, presented Charles with some blue crocus bulbs as he told members of the public that his new grandson, George, was 'doing very well'.
Her mother, Victoria Holt, from Wymondham, Norfolk, said: 'He seemed very interested in Evelyn and gave her lots of attention.'
Having fun: The couple share a joke at the flower show
Flower power: They admire the colour and scent of some roses
Dame Maggie Smith was among the royal couple's guests at the show, along with Dame Judi Dench and television food critic Matthew Fort who also attended a charity concert in the village of Salle last night.
The Duchess was heard commenting on the weather, remarking how the event normally enjoyed bright sunshine, while she posed for a picture with Jack Russell, Scooby.
Scooby's owner, Yvonne Harradine, 66, from Terrington St Clement, Norfolk, said: 'She likes Jack Russells and I took a picture of her with Scooby last year but when it came out I realised I had cut her head off. It was very kind of her to agree to pose for another picture and I think it worked this time.'
The Sandringham Flower Show takes place every year in Sandringham Park against the backdrop of Sandringham House.
The couple, who arrived and left by horse and cart, viewed competition entries including vegetables, fruit, flowers and floral art.
Showers: Smiling Camilla didn't let the rain dampen her day
There is nothing like a Dame: Dame Maggie Smith, left, and Dame Judi Dench also attended the show in Norfolk
The profits from each show are donated to local charities and since 1977 the show committee has given more than £500,000 to good causes.
The prince took particular interest in a garden to honour the Prince's Trust. It showed an area of wilderness linked by bridge to a more ordered garden to symbolise the part the trust plays in turning young people's lives around.
The profits from each show are donated to local charities and since 1977 the show committee has given more than £500,000 to good causes.
The prince took particular interest in a garden to honour the Prince's Trust. It showed an area of wilderness linked by bridge to a more ordered garden to symbolise the part the trust plays in turning young people's lives around.