Just a piece of advice from a person who has been friends with a Kayla (or even more than one) for most of her life.
Instead of using your energy to convince your daughter to stay away from Kayla, use it to help your daughter to grow a titanium spine and a firm self esteem. Because she will come across more than one Kayla in her life. They grow like weed.

Once youīve got rid of one Kayla, three grow back.

In my opinion, Kaylas have to be pittied. They lack self-esteem, so they have to make someone small, just to have the feeling to be superior.
Iīve been friends with a one-upper (oh, how I love this expression!) since childhood days. I was an overweight, shy and self-concious child and was always very intimidated by her comments. Bigger house, better at school, richer parents, prettier face, smarter brain, lying and boasting --> just kayla-esque behaviour as you described. Behaviour getting almost unbearable through our teenage years and early 20s.
Since then, with the help of relatives, friends and overall positive experiences, Iīve developed a quite impregnable self-esteem. I simply stopped caring about what others think of me. I will never be able to reach their standards, but as long as Iīm able to reach the standards Iīve set for myself, I live a rather carefree life.

I will never be the smartest, prettiest, wealthiest person in the world, so why care.
Friend has changed a lot during the past years as well. Becoming a nicer person. Thatīs why Iīm still friends with her. But sometimes her inner Kayla shows again. For these situations Iīve learned to give her a sip of her own medicine. I still remember our childhood days and now it is time to pay back.

(You know, I forgive, but I never forget.)
She still has the need to boast and challenge me, but I take me revenge in simply not being impressed and making fun of her. Just let me give a few examples. (I know, some of my comments are mean and probably rude, but ..he.. she didnīt care about my feelings back then either.)
- Friend and me trying on same dress. Both looked good in it. (I migh add, Iīm still on the heavier side but with better proportions than she has.)
Friend: "I canīt buy this dress. My bum looks sooo incredibly big in this dress." (Which by the way is not true.) looks at me. "Donīt you think this is the problem with the dress for you as well??" ( Lady, my bum looks big in absolutely everything.

)
Me: "I canīt tell. Iīm physically not able to see my own bum. So, if it looks too big that might be more of a problem for the person walking behind me. And should it be necessary, Iīll just lean against a wall." and bought the dress.
- Constant topic of designer clothes. (I love to shop. But I love to have lots of clothes for less money, while she thinks that clothes from certain high-price brands make her a better person.)
Friend: "Look, Iīve bought these *needlessly high-priced* designer jeans for $ 400 . Iīm so glad, I can afford that."
Me: "Well, I guess so, because you just earn a little less than I do." (I know, this is mean and rude, but after boasting about how much she earns for years, she recently found out that I actually earn more than she does.

)
Friend: "Well, but arenīt you impressed that I bought them?" (Yes, she really used "impressed.")
Me: "Impressed that you paid $ 400 for a pair of jeans? No, I would be impressed if youīve paid $ 50 for this designer jeans, but $ 400 is just .... well, YOU can afford it. Have you tasted the bean-dip yet?"
- The mother of another friend is also into designer clothes, but her weight is constantly yoyo-ing. So he has them in all sizes. Everytime she looses weight, my friend gets a bunch of clothes which donīt fit her mum anymore. Friend is taller and smaller than mum and I, so I always end up getting the clothes..for free.

Mum is so delighted that at least someone is still wearing her beloved clothes.
So, one-upper friendīs favorite sentence everytime Iīm wearing one of the pieces: "Why are YOU wearing a *piece of clothes* from *designer brand*? I didnīt know you can afford that?"
Me (whispering): "You know Iīve got one of these sugar daddies who gives me expensive things for playing scrabble." (The look on her face is priceless.

)
Sorry for making this post so long, but Iīve enjoyed to recapitulate these stories.

But to cut a long story short: You probably canīt shield your daughter from all the Kaylas in her life, but you can give her the tools to handle them.