The fashion designer, who was filmed talking about her friendship with the supermodel for Kate's new Topshop clothing collection, joked about her unusual looks, intimate conversations with the star and her love of fashion.
In the video, Vivienne, 73, says: ''She's got a big aura that she draws you into. Every time she speaks to me I feel like we're in a conspiracy. She is so intimate that you just want to know what are we going to be doing together.''
Talking about her favourite of Kate's features, she added: ''I have never seen anybody with more far apart eyes than she has, there's something so attractive about her.''
Vivienne also described Kate as one of the ''most stylish people on the planet'' and someone who loves fashion and understands clothes in way others don't.
She added: ''She knows how to work clothes. She's just got it.'
In the other video, musician Bobby Gillespie talks about his friendship with Kate, 40, and claims she's ''always up for fun''.
He explained: ''She is pretty free - quite a free soul. She's pretty experimental and fearless in the way she lives her life.''
Talking about what makes her stand out, he said: ''Apart from the fact that she's an amazing model and is really beautiful, she's also got this other quality that people relate to.
''I don't think people think she is unattainable or untouchable, although she kind of is. I think people think she could come for our street, she's like one of us.''