Shiplap is quite dated at this point. Those fixer upper TV shows that installed shiplap in every home are already several years old. Your designer is behind the times and borrowing ideas from passé TV. In addition, I don't think shiplap works well in a kitchen because of the possibility of moisture and/or critters getting behind the slats.

Also, wouldn't "concrete shiplap" just look like the concrete was poured into an old style wood plank form? I think that would be kinda... coarse and grody for an interior space. Would you paint it? Could you just do wood (consider a not-shiplap such as beadboard) for everywhere except behind the stove, were you could do a nice tile or stone backdrop?

I did hardieboard in a horizontal planked style (not exactly shiplap, but sort of) for a non-combustible material behind a wood-burning stove. It was a year or two ago, so I'm a bit fuzzy, but I think we just used a finish nailer to nail it in place.