Florist arrangements or creating a wedding cake is part of an art form.
No, it isn't.
It's a business that operates as a public accommodation. Making cakes is a commercial service, not an expressive act. When the baker writes "Congrats Tim and Jim on their wedding," that is no more an expressive act than someone walking into Kinko's and using their photocopiers to print hundreds of flyers.
Something similar happened with the Elane Photography case. The photographer refused to photograph a wedding specifically because of the gender and sexual orientation of the participants (a gay couple). The New Mexico court ruled that because Elane Photography advertised its services directly to the public, it was operating as a public accommodation. It rejected the idea that expressive professions were exempt from the civil rights laws.
How many artists refused to participate in Trump’s inauguration? Shouldn’t Trump sue because those artists discriminated against him?
Nope. Those artists do not operate as public accommodations. Civil rights laws do not apply.
He is in an unique classification as president so he has a case.
Not even close.
In addition to the above issue: "Elected official" is not a protected classification. Maybe you could get away with that in California, where civil rights laws have been interpreted broadly. But that's not going to fly in most US states.
An artist also said on tv that he refused to design Mrs. Trump dress, isn't that another discrimination case?
You'd have to make the case that the designer operates as a public accommodation. If they do not advertise haute couture or custom design services to the public, or have a history of being exclusive, then you aren't likely to prove in court that they operate as a public accommodation.
E.g. Andre Leon Talley doesn't operate as a public accommodation. He doesn't advertise his services as a stylist, he has a history of exclusivity, he doesn't have a storefront open to the public. Same for John Wu's services as a designer.
I realize civil rights law is complex (and what I'm saying just scratches the surface), but next time it might help to know what you're talking about before making such suggestions.