I would say Barbie and Ken's love language is spending time together, getting help and affirmation from each other, and giving gifts to each other.
https://www.youtube.com/watch?v=ScBqGEVot6Y&ab_channel=ovaminyu
In A Fashion Fairytale, Raquelle makes Barbie think Ken has broken up with her. Barbie goes to Paris to get away from all the drama in her life (including being fired from her job). Someone tells Ken he has to do a "grand romantic gesture" to get her back, so Ken goes alllll the way to Paris to find Barbie.
Barbie: You showed up at the perfect time. And all the way to Paris. It's the most romantic thing I could ever imagine.
Ken: That's what I wanted. A grand romantic gesture to prove how much I love you. And I do.
Barbie: I love you, too.
In A Fairy Secret, Barbie rescues Ken from a fairy that wants to marry him.
In Princess Adventure, Ken wants to tell Barbie that he likes her but he's too shy.
Some Dreamhouse Adventures moments:
"Roof Fairy" episode - Barbie calls Ken for help. Before she can explain what she needs help with, Ken says he only wants to know when and where she needs him.
"Balancing Act" - Barbie wants to talk about how she's feeling with someone who understands her the most, so she goes to Ken. When Barbie is sad later on, Ken helps throw her a pool party.
"Life Can Be a Dream" - Barbie and Ken dance together at the end of Barbie's dream.
"Time Will Tell" - This is the biggest Barbie and Ken episode yet. They have to do an escape room together and there's a lot of cute moments. People tell them they have chemistry and Barbie thinks her and Ken are "teammates, partners, friends", but time will tell if they become a couple.
In "Getaway and Got Away", Ken applies for a lifeguarding job at a spa so he gives Barbie a free pass. When he gets fired, Barbie comforts him and says "You're the best lifeguard I know! You're responsible, and brave, and kind, and ALWAYS right there when you're needed." Ken gets shy after she says this.
There's also "Dreamhouse Holidays" from Go Team Roberts season 2. "While the family prepare for the holidays, Ken and Barbie discover the true meaning of friendship when they find the perfect gifts for one another."
And "Barbie's Dance Dilemma" where Barbie has mixed feelings about Ken going to the school dance with another girl.
Also Ken is always helping Barbie with things!
The Barbie and Ken Love the Ocean vlog is so cute at the beginning :< I think Ken got her the bracelet. There's a lot of vlogs of them together, but this is the first one that comes to mind. I think Ken might be her most featured guest? In another vlog, someone has given Barbie flowers, and I think it was Ken.
Barbie and Ken going to prom together:
Barbie's friends and family help Ken do a promposal for Barbie, because he's too shy to do it by himself :< Barbie says Ken was "charming", he thought she looked "beautiful" even though she was only wearing a basic outfit with jeans, and she had "the best night of my life!"
2:20 Barbie and Ken used to meet up and talk about life when they were younger.
https://www.youtube.com/watch?v=Nn9oaq0lFpI
Barbie accidentally calls Ken her boyfriend!
https://www.youtube.com/watch?v=1lHmZJx3Fp8
Ken thinks Barbie said she loves him and she gets embarrassed.
https://www.youtube.com/watch?v=3x06kfHnjWs&ab_channel=Barbie
Barbie and Ken make a cake that says "Karbie" on it.
https://www.youtube.com/watch?v=KWsZh9XE9sQ&ab_channel=Barbie
Barbie and Ken's hands touch and they get embarrassed.
https://www.youtube.com/watch?v=u1JQwwWfngQ&ab_channel=Barbie
1:03 "Who is most likely to have a secret crush?" Harper points and Barbie and Ken and I think she mouths "it's them".
More vlogs: