I am replacing a carpet for a person who has incontinece. What would be the best flooring to install to repel urine? Vinyl, linoleum, painted concrete?

This may not be what you want to hear but that person needs Depends. I took care of a 96 year old and repeated cleaning up of urine is not fun and can be prevented with pads. To answer your question, any of the seamless products you mention would work but cost and looks will vary greatly.

She does use pull-ups, but she is Developementally Disabled and sometimes it's due to behavior. She needs a floor that is easy to keep clean.

I mean unless the floor under the carpet is concrete you don't really have that choice.

But any of those will repell urine